%hide %html <h1>Exercise 1</h1> Just using Sage for the difficult involution.

Exercise 1

Just using Sage for the difficult involution.

Exercise 1

Just using Sage for the difficult involution.

var('x') u = function('u',x) ux = diff(u,x) uxx = diff(ux,x) uxxx = diff(uxx,x) uxxxx = diff(uxxx,x)

u_integrand = u^4*ux/6 + u*ux^3/2 + u^2*ux^2 + 3*u*ux*uxxxx/5 + u^3*uxxx/6 + ux^2*uxxx/2 + u*ux*uxxx + 3*uxxx*uxxxx/5

show(u_integrand.integrate(x))

\newcommand{\Bold}[1]{\mathbf{#1}}\frac{1}{30} \, u\left(x\right)^{5} + \int \frac{1}{6} \, u\left(x\right)^{3} D[0, 0, 0]\left(u\right)\left(x\right) + u\left(x\right)^{2} D[0]\left(u\right)\left(x\right)^{2} + \frac{1}{2} \, u\left(x\right) D[0]\left(u\right)\left(x\right)^{3} + u\left(x\right) D[0]\left(u\right)\left(x\right) D[0, 0, 0]\left(u\right)\left(x\right) + \frac{3}{5} \, u\left(x\right) D[0]\left(u\right)\left(x\right) D[0, 0, 0, 0]\left(u\right)\left(x\right) + \frac{1}{2} \, D[0]\left(u\right)\left(x\right)^{2} D[0, 0, 0]\left(u\right)\left(x\right) + \frac{3}{5} \, D[0, 0, 0]\left(u\right)\left(x\right) D[0, 0, 0, 0]\left(u\right)\left(x\right)\,{d x}

\newcommand{\Bold}[1]{\mathbf{#1}}\frac{1}{30} \, u\left(x\right)^{5} + \int \frac{1}{6} \, u\left(x\right)^{3} D[0, 0, 0]\left(u\right)\left(x\right) + u\left(x\right)^{2} D[0]\left(u\right)\left(x\right)^{2} + \frac{1}{2} \, u\left(x\right) D[0]\left(u\right)\left(x\right)^{3} + u\left(x\right) D[0]\left(u\right)\left(x\right) D[0, 0, 0]\left(u\right)\left(x\right) + \frac{3}{5} \, u\left(x\right) D[0]\left(u\right)\left(x\right) D[0, 0, 0, 0]\left(u\right)\left(x\right) + \frac{1}{2} \, D[0]\left(u\right)\left(x\right)^{2} D[0, 0, 0]\left(u\right)\left(x\right) + \frac{3}{5} \, D[0, 0, 0]\left(u\right)\left(x\right) D[0, 0, 0, 0]\left(u\right)\left(x\right)\,{d x}

%hide %html <h1>Exercise 4</h1> For a suitable $k$, <p align="center">$U(x) = 2 \partial_x^2 \log (1 + e^{kx+\alpha})$</p> is a solution to <p align="center">$6uu_x + u_{xxx} + c_0u_x = 0$</p> for a suitable choice of $c_0$ in terms of $k$.

Exercise 4

For a suitable k,

U(x) = 2 \partial_x^2 \log (1 + e^{kx+\alpha})

is a solution to

6uu_x + u_{xxx} + c_0u_x = 0

for a suitable choice of c_0 in terms of k.

Exercise 4

For a suitable k,

U(x) = 2 \partial_x^2 \log (1 + e^{kx+\alpha})

is a solution to

6uu_x + u_{xxx} + c_0u_x = 0

for a suitable choice of c_0 in terms of k.

var('x,k,alpha,c_0') theta = log(1 + exp(k*x + alpha)) U = 2*theta.derivative(x,2) U = U.simplify_exp() U

\newcommand{\Bold}[1]{\mathbf{#1}}\frac{2 \, k^{2} e^{\left(k x + \alpha\right)}}{2 \, e^{\left(k x + \alpha\right)} + e^{\left(2 \, k x + 2 \, \alpha\right)} + 1}

\newcommand{\Bold}[1]{\mathbf{#1}}\frac{2 \, k^{2} e^{\left(k x + \alpha\right)}}{2 \, e^{\left(k x + \alpha\right)} + e^{\left(2 \, k x + 2 \, \alpha\right)} + 1}

V = 6*U*U.derivative(x,1) + U.derivative(x,3) + c_0 * U.derivative(x,1) V = V.simplify_rational() V

\newcommand{\Bold}[1]{\mathbf{#1}}\frac{2 \, {\left({\left(k^{5} e^{\alpha} + c_{0} k^{3} e^{\alpha}\right)} e^{\left(k x\right)} - {\left(k^{5} e^{\left(2 \, \alpha\right)} + c_{0} k^{3} e^{\left(2 \, \alpha\right)}\right)} e^{\left(2 \, k x\right)}\right)}}{3 \, e^{\left(k x + \alpha\right)} + 3 \, e^{\left(2 \, k x + 2 \, \alpha\right)} + e^{\left(3 \, k x + 3 \, \alpha\right)} + 1}

\newcommand{\Bold}[1]{\mathbf{#1}}\frac{2 \, {\left({\left(k^{5} e^{\alpha} + c_{0} k^{3} e^{\alpha}\right)} e^{\left(k x\right)} - {\left(k^{5} e^{\left(2 \, \alpha\right)} + c_{0} k^{3} e^{\left(2 \, \alpha\right)}\right)} e^{\left(2 \, k x\right)}\right)}}{3 \, e^{\left(k x + \alpha\right)} + 3 \, e^{\left(2 \, k x + 2 \, \alpha\right)} + e^{\left(3 \, k x + 3 \, \alpha\right)} + 1}

V.solve(c_0)

\newcommand{\Bold}[1]{\mathbf{#1}}\left[c_{0} = -k^{2}\right]

\newcommand{\Bold}[1]{\mathbf{#1}}\left[c_{0} = -k^{2}\right]

%hide %html So $U(x)$ is a solution to <p align="center">$6uu_x + u_{xxx} - k^2u_x = 0$</p> for all $k$. Now, we let $u(x,t_1,t_2,t_3,\ldots) = U(x)|_{\alpha = \alpha(t_1,t_2,t_3,\ldots)}$ and determine the dependence of $\alpha$ on $t_1,t_2,t_3$ such that this $u$ is simultaneously a solution of the first, second, and third KdV equations.

So U(x) is a solution to

6uu_x + u_{xxx} - k^2u_x = 0

for all k. Now, we let u(x,t_1,t_2,t_3,\ldots) = U(x)|_{\alpha = \alpha(t_1,t_2,t_3,\ldots)} and determine the dependence of \alpha on t_1,t_2,t_3 such that this u is simultaneously a solution of the first, second, and third KdV equations.

So U(x) is a solution to

6uu_x + u_{xxx} - k^2u_x = 0

for all k. Now, we let u(x,t_1,t_2,t_3,\ldots) = U(x)|_{\alpha = \alpha(t_1,t_2,t_3,\ldots)} and determine the dependence of \alpha on t_1,t_2,t_3 such that this u is simultaneously a solution of the first, second, and third KdV equations.

var('t_1,t_2,t_3') var('x,k,alpha') alpha = function('alpha', t_1,t_2,t_3) theta = log(1 + exp(k*x + alpha)) U = 2*theta.derivative(x,2) U = U.simplify_exp() U_x = U.derivative(x,1) U_xx = U.derivative(x,2) U_xxx = U.derivative(x,3) show(U)

\newcommand{\Bold}[1]{\mathbf{#1}}\frac{2 \, k^{2} e^{\left(k x + \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)}}{2 \, e^{\left(k x + \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} + e^{\left(2 \, k x + 2 \, \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} + 1}

\newcommand{\Bold}[1]{\mathbf{#1}}\frac{2 \, k^{2} e^{\left(k x + \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)}}{2 \, e^{\left(k x + \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} + e^{\left(2 \, k x + 2 \, \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} + 1}

U_t_1 = diff(U,t_1).simplify_full() RHS_t_1 = (6*U*U_x + U_xxx).simplify_full() show(U_t_1) show(RHS_t_1)

\newcommand{\Bold}[1]{\mathbf{#1}}\frac{2 \, {\left(k^{2} e^{\left(k x + \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} D[0]\left(\alpha\right)\left(t_{1}, t_{2}, t_{3}\right) - k^{2} e^{\left(2 \, k x + 2 \, \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} D[0]\left(\alpha\right)\left(t_{1}, t_{2}, t_{3}\right)\right)}}{3 \, e^{\left(k x + \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} + 3 \, e^{\left(2 \, k x + 2 \, \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} + e^{\left(3 \, k x + 3 \, \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} + 1}
\newcommand{\Bold}[1]{\mathbf{#1}}\frac{2 \, {\left(k^{5} e^{\left(k x + \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} - k^{5} e^{\left(2 \, k x + 2 \, \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)}\right)}}{3 \, e^{\left(k x + \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} + 3 \, e^{\left(2 \, k x + 2 \, \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} + e^{\left(3 \, k x + 3 \, \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} + 1}

\newcommand{\Bold}[1]{\mathbf{#1}}\frac{2 \, {\left(k^{2} e^{\left(k x + \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} D[0]\left(\alpha\right)\left(t_{1}, t_{2}, t_{3}\right) - k^{2} e^{\left(2 \, k x + 2 \, \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} D[0]\left(\alpha\right)\left(t_{1}, t_{2}, t_{3}\right)\right)}}{3 \, e^{\left(k x + \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} + 3 \, e^{\left(2 \, k x + 2 \, \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} + e^{\left(3 \, k x + 3 \, \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} + 1}
\newcommand{\Bold}[1]{\mathbf{#1}}\frac{2 \, {\left(k^{5} e^{\left(k x + \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} - k^{5} e^{\left(2 \, k x + 2 \, \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)}\right)}}{3 \, e^{\left(k x + \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} + 3 \, e^{\left(2 \, k x + 2 \, \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} + e^{\left(3 \, k x + 3 \, \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} + 1}

U_t_2 = diff(U,t_2).simplify_exp() RHS_t_2 = (30*U^2*U_x + 20*U_x*U_xx + 10*U*U_xxx + U.derivative(x,5)).simplify_full() show(U_t_2) show(RHS_t_2)

\newcommand{\Bold}[1]{\mathbf{#1}}\frac{2 \, {\left(k^{2} e^{\left(k x + \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} D[1]\left(\alpha\right)\left(t_{1}, t_{2}, t_{3}\right) - k^{2} e^{\left(2 \, k x + 2 \, \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} D[1]\left(\alpha\right)\left(t_{1}, t_{2}, t_{3}\right)\right)}}{3 \, e^{\left(k x + \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} + 3 \, e^{\left(2 \, k x + 2 \, \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} + e^{\left(3 \, k x + 3 \, \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} + 1}
\newcommand{\Bold}[1]{\mathbf{#1}}\frac{2 \, {\left(k^{7} e^{\left(k x + \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} - k^{7} e^{\left(2 \, k x + 2 \, \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)}\right)}}{3 \, e^{\left(k x + \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} + 3 \, e^{\left(2 \, k x + 2 \, \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} + e^{\left(3 \, k x + 3 \, \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} + 1}

\newcommand{\Bold}[1]{\mathbf{#1}}\frac{2 \, {\left(k^{2} e^{\left(k x + \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} D[1]\left(\alpha\right)\left(t_{1}, t_{2}, t_{3}\right) - k^{2} e^{\left(2 \, k x + 2 \, \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} D[1]\left(\alpha\right)\left(t_{1}, t_{2}, t_{3}\right)\right)}}{3 \, e^{\left(k x + \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} + 3 \, e^{\left(2 \, k x + 2 \, \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} + e^{\left(3 \, k x + 3 \, \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} + 1}
\newcommand{\Bold}[1]{\mathbf{#1}}\frac{2 \, {\left(k^{7} e^{\left(k x + \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} - k^{7} e^{\left(2 \, k x + 2 \, \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)}\right)}}{3 \, e^{\left(k x + \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} + 3 \, e^{\left(2 \, k x + 2 \, \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} + e^{\left(3 \, k x + 3 \, \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} + 1}

U_t_3 = diff(U,t_3).simplify_full() RHS_t_3 = (140*U^3*U_x + 70*U_x^3 + 280*U*U_x*U_xx + 70*U_xx*U_xxx + 70*U^2*U_xxx + 42*U_x*U.derivative(x,4) + 14*U*U.derivative(x,5) + U.derivative(x,7)).simplify_full() show(U_t_3) show(RHS_t_3)

\newcommand{\Bold}[1]{\mathbf{#1}}\frac{2 \, {\left(k^{2} e^{\left(k x + \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} D[2]\left(\alpha\right)\left(t_{1}, t_{2}, t_{3}\right) - k^{2} e^{\left(2 \, k x + 2 \, \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} D[2]\left(\alpha\right)\left(t_{1}, t_{2}, t_{3}\right)\right)}}{3 \, e^{\left(k x + \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} + 3 \, e^{\left(2 \, k x + 2 \, \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} + e^{\left(3 \, k x + 3 \, \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} + 1}
\newcommand{\Bold}[1]{\mathbf{#1}}\frac{2 \, {\left(k^{9} e^{\left(k x + \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} - k^{9} e^{\left(2 \, k x + 2 \, \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)}\right)}}{3 \, e^{\left(k x + \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} + 3 \, e^{\left(2 \, k x + 2 \, \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} + e^{\left(3 \, k x + 3 \, \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} + 1}

\newcommand{\Bold}[1]{\mathbf{#1}}\frac{2 \, {\left(k^{2} e^{\left(k x + \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} D[2]\left(\alpha\right)\left(t_{1}, t_{2}, t_{3}\right) - k^{2} e^{\left(2 \, k x + 2 \, \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} D[2]\left(\alpha\right)\left(t_{1}, t_{2}, t_{3}\right)\right)}}{3 \, e^{\left(k x + \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} + 3 \, e^{\left(2 \, k x + 2 \, \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} + e^{\left(3 \, k x + 3 \, \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} + 1}
\newcommand{\Bold}[1]{\mathbf{#1}}\frac{2 \, {\left(k^{9} e^{\left(k x + \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} - k^{9} e^{\left(2 \, k x + 2 \, \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)}\right)}}{3 \, e^{\left(k x + \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} + 3 \, e^{\left(2 \, k x + 2 \, \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} + e^{\left(3 \, k x + 3 \, \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} + 1}

U_t_is = [U_t_1,U_t_2,U_t_3] RHS_t_is = [RHS_t_1,RHS_t_2,RHS_t_3] Unums = [] RHSnums = [] for U_t_i,RHS_t_i in zip(U_t_is,RHS_t_is): Unums.append(U_t_i.numerator()) RHSnums.append(RHS_t_i.numerator())

show(Unums[0]) show(RHSnums[0])

\newcommand{\Bold}[1]{\mathbf{#1}}2 \, k^{2} e^{\left(k x + \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} D[0]\left(\alpha\right)\left(t_{1}, t_{2}, t_{3}\right) - 2 \, k^{2} e^{\left(2 \, k x + 2 \, \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} D[0]\left(\alpha\right)\left(t_{1}, t_{2}, t_{3}\right)
\newcommand{\Bold}[1]{\mathbf{#1}}2 \, k^{5} e^{\left(k x + \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} - 2 \, k^{5} e^{\left(2 \, k x + 2 \, \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)}

\newcommand{\Bold}[1]{\mathbf{#1}}2 \, k^{2} e^{\left(k x + \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} D[0]\left(\alpha\right)\left(t_{1}, t_{2}, t_{3}\right) - 2 \, k^{2} e^{\left(2 \, k x + 2 \, \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} D[0]\left(\alpha\right)\left(t_{1}, t_{2}, t_{3}\right)
\newcommand{\Bold}[1]{\mathbf{#1}}2 \, k^{5} e^{\left(k x + \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} - 2 \, k^{5} e^{\left(2 \, k x + 2 \, \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)}

show(Unums[1]) show(RHSnums[1])

\newcommand{\Bold}[1]{\mathbf{#1}}2 \, k^{2} e^{\left(k x + \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} D[1]\left(\alpha\right)\left(t_{1}, t_{2}, t_{3}\right) - 2 \, k^{2} e^{\left(2 \, k x + 2 \, \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} D[1]\left(\alpha\right)\left(t_{1}, t_{2}, t_{3}\right)
\newcommand{\Bold}[1]{\mathbf{#1}}2 \, k^{7} e^{\left(k x + \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} - 2 \, k^{7} e^{\left(2 \, k x + 2 \, \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)}

\newcommand{\Bold}[1]{\mathbf{#1}}2 \, k^{2} e^{\left(k x + \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} D[1]\left(\alpha\right)\left(t_{1}, t_{2}, t_{3}\right) - 2 \, k^{2} e^{\left(2 \, k x + 2 \, \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} D[1]\left(\alpha\right)\left(t_{1}, t_{2}, t_{3}\right)
\newcommand{\Bold}[1]{\mathbf{#1}}2 \, k^{7} e^{\left(k x + \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} - 2 \, k^{7} e^{\left(2 \, k x + 2 \, \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)}

show(Unums[2]) show(RHSnums[2])

\newcommand{\Bold}[1]{\mathbf{#1}}2 \, k^{2} e^{\left(k x + \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} D[2]\left(\alpha\right)\left(t_{1}, t_{2}, t_{3}\right) - 2 \, k^{2} e^{\left(2 \, k x + 2 \, \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} D[2]\left(\alpha\right)\left(t_{1}, t_{2}, t_{3}\right)
\newcommand{\Bold}[1]{\mathbf{#1}}2 \, k^{9} e^{\left(k x + \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} - 2 \, k^{9} e^{\left(2 \, k x + 2 \, \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)}

\newcommand{\Bold}[1]{\mathbf{#1}}2 \, k^{2} e^{\left(k x + \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} D[2]\left(\alpha\right)\left(t_{1}, t_{2}, t_{3}\right) - 2 \, k^{2} e^{\left(2 \, k x + 2 \, \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} D[2]\left(\alpha\right)\left(t_{1}, t_{2}, t_{3}\right)
\newcommand{\Bold}[1]{\mathbf{#1}}2 \, k^{9} e^{\left(k x + \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} - 2 \, k^{9} e^{\left(2 \, k x + 2 \, \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)}

show(Unums[0].factor())

\newcommand{\Bold}[1]{\mathbf{#1}}-2 \, {\left(e^{\left(k x + \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} - 1\right)} k^{2} e^{\left(k x + \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} D[0]\left(\alpha\right)\left(t_{1}, t_{2}, t_{3}\right)

\newcommand{\Bold}[1]{\mathbf{#1}}-2 \, {\left(e^{\left(k x + \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} - 1\right)} k^{2} e^{\left(k x + \alpha\left(t_{1}, t_{2}, t_{3}\right)\right)} D[0]\left(\alpha\right)\left(t_{1}, t_{2}, t_{3}\right)

%hide %html <h1>Exercise 5</h1>

Exercise 5

var('x,k_1,k_2,alpha,beta,c_0,c_1')

\newcommand{\Bold}[1]{\mathbf{#1}}\left(x, k_{1}, k_{2}, \alpha, \beta, c_{0}, c_{1}\right)

\newcommand{\Bold}[1]{\mathbf{#1}}\left(x, k_{1}, k_{2}, \alpha, \beta, c_{0}, c_{1}\right)

V = log(1 + exp(k_1*x + alpha) + exp(k_2*x + beta) + (k_1-k_2)^2/(k_1+k_2)^2 * exp(k_1*x + k_2*x + alpha + beta)) U = 2*V.derivative(x,2) Ux = diff(U,x) Uxx = diff(Ux,x) Uxxx = diff(Uxx,x) Uxxxx = diff(Uxxx,x) Uxxxxx = diff(Uxxxx,x)

bigeqn = 30*U^2*Ux + 20*Ux*Uxx + 10*U*Uxxx + Uxxxxx + c_1*(6*U*Ux+Uxxx) + c_0*Ux

bigeqn = bigeqn.simplify_rational() show(bigeqn)

\newcommand{\Bold}[1]{\mathbf{#1}}-\frac{2 \, {\left({\left({\left(k_{1}^{13} e^{\left(2 \, \alpha + 3 \, \beta\right)} + c_{1} k_{1}^{11} e^{\left(2 \, \alpha + 3 \, \beta\right)} + c_{0} k_{1}^{9} e^{\left(2 \, \alpha + 3 \, \beta\right)} + {\left(k_{1}^{7} e^{\left(2 \, \alpha + 3 \, \beta\right)} + c_{1} k_{1}^{5} e^{\left(2 \, \alpha + 3 \, \beta\right)} + c_{0} k_{1}^{3} e^{\left(2 \, \alpha + 3 \, \beta\right)}\right)} k_{2}^{6} - 2 \, {\left(k_{1}^{8} e^{\left(2 \, \alpha + 3 \, \beta\right)} + c_{1} k_{1}^{6} e^{\left(2 \, \alpha + 3 \, \beta\right)} + c_{0} k_{1}^{4} e^{\left(2 \, \alpha + 3 \, \beta\right)}\right)} k_{2}^{5} - {\left(k_{1}^{9} e^{\left(2 \, \alpha + 3 \, \beta\right)} + c_{1} k_{1}^{7} e^{\left(2 \, \alpha + 3 \, \beta\right)} + c_{0} k_{1}^{5} e^{\left(2 \, \alpha + 3 \, \beta\right)}\right)} k_{2}^{4} + 4 \, {\left(k_{1}^{10} e^{\left(2 \, \alpha + 3 \, \beta\right)} + c_{1} k_{1}^{8} e^{\left(2 \, \alpha + 3 \, \beta\right)} + c_{0} k_{1}^{6} e^{\left(2 \, \alpha + 3 \, \beta\right)}\right)} k_{2}^{3} - {\left(k_{1}^{11} e^{\left(2 \, \alpha + 3 \, \beta\right)} + c_{1} k_{1}^{9} e^{\left(2 \, \alpha + 3 \, \beta\right)} + c_{0} k_{1}^{7} e^{\left(2 \, \alpha + 3 \, \beta\right)}\right)} k_{2}^{2} - 2 \, {\left(k_{1}^{12} e^{\left(2 \, \alpha + 3 \, \beta\right)} + c_{1} k_{1}^{10} e^{\left(2 \, \alpha + 3 \, \beta\right)} + c_{0} k_{1}^{8} e^{\left(2 \, \alpha + 3 \, \beta\right)}\right)} k_{2}\right)} e^{\left(2 \, k_{1} x\right)} - {\left(k_{1}^{13} e^{\left(\alpha + 3 \, \beta\right)} + c_{1} k_{1}^{11} e^{\left(\alpha + 3 \, \beta\right)} + c_{0} k_{1}^{9} e^{\left(\alpha + 3 \, \beta\right)} + {\left(k_{1}^{7} e^{\left(\alpha + 3 \, \beta\right)} + c_{1} k_{1}^{5} e^{\left(\alpha + 3 \, \beta\right)} + c_{0} k_{1}^{3} e^{\left(\alpha + 3 \, \beta\right)}\right)} k_{2}^{6} + 2 \, {\left(k_{1}^{8} e^{\left(\alpha + 3 \, \beta\right)} + c_{1} k_{1}^{6} e^{\left(\alpha + 3 \, \beta\right)} + c_{0} k_{1}^{4} e^{\left(\alpha + 3 \, \beta\right)}\right)} k_{2}^{5} - {\left(k_{1}^{9} e^{\left(\alpha + 3 \, \beta\right)} + c_{1} k_{1}^{7} e^{\left(\alpha + 3 \, \beta\right)} + c_{0} k_{1}^{5} e^{\left(\alpha + 3 \, \beta\right)}\right)} k_{2}^{4} - 4 \, {\left(k_{1}^{10} e^{\left(\alpha + 3 \, \beta\right)} + c_{1} k_{1}^{8} e^{\left(\alpha + 3 \, \beta\right)} + c_{0} k_{1}^{6} e^{\left(\alpha + 3 \, \beta\right)}\right)} k_{2}^{3} - {\left(k_{1}^{11} e^{\left(\alpha + 3 \, \beta\right)} + c_{1} k_{1}^{9} e^{\left(\alpha + 3 \, \beta\right)} + c_{0} k_{1}^{7} e^{\left(\alpha + 3 \, \beta\right)}\right)} k_{2}^{2} + 2 \, {\left(k_{1}^{12} e^{\left(\alpha + 3 \, \beta\right)} + c_{1} k_{1}^{10} e^{\left(\alpha + 3 \, \beta\right)} + c_{0} k_{1}^{8} e^{\left(\alpha + 3 \, \beta\right)}\right)} k_{2}\right)} e^{\left(k_{1} x\right)}\right)} e^{\left(3 \, k_{2} x\right)} - {\left(k_{1}^{13} e^{\alpha} + c_{1} k_{1}^{11} e^{\alpha} + c_{0} k_{1}^{9} e^{\alpha} + {\left(k_{1}^{7} e^{\alpha} + c_{1} k_{1}^{5} e^{\alpha} + c_{0} k_{1}^{3} e^{\alpha}\right)} k_{2}^{6} + 6 \, {\left(k_{1}^{8} e^{\alpha} + c_{1} k_{1}^{6} e^{\alpha} + c_{0} k_{1}^{4} e^{\alpha}\right)} k_{2}^{5} + 15 \, {\left(k_{1}^{9} e^{\alpha} + c_{1} k_{1}^{7} e^{\alpha} + c_{0} k_{1}^{5} e^{\alpha}\right)} k_{2}^{4} + 20 \, {\left(k_{1}^{10} e^{\alpha} + c_{1} k_{1}^{8} e^{\alpha} + c_{0} k_{1}^{6} e^{\alpha}\right)} k_{2}^{3} + 15 \, {\left(k_{1}^{11} e^{\alpha} + c_{1} k_{1}^{9} e^{\alpha} + c_{0} k_{1}^{7} e^{\alpha}\right)} k_{2}^{2} + 6 \, {\left(k_{1}^{12} e^{\alpha} + c_{1} k_{1}^{10} e^{\alpha} + c_{0} k_{1}^{8} e^{\alpha}\right)} k_{2}\right)} e^{\left(k_{1} x\right)} + {\left(k_{1}^{13} e^{\left(2 \, \alpha\right)} + c_{1} k_{1}^{11} e^{\left(2 \, \alpha\right)} + c_{0} k_{1}^{9} e^{\left(2 \, \alpha\right)} + {\left(k_{1}^{7} e^{\left(2 \, \alpha\right)} + c_{1} k_{1}^{5} e^{\left(2 \, \alpha\right)} + c_{0} k_{1}^{3} e^{\left(2 \, \alpha\right)}\right)} k_{2}^{6} + 6 \, {\left(k_{1}^{8} e^{\left(2 \, \alpha\right)} + c_{1} k_{1}^{6} e^{\left(2 \, \alpha\right)} + c_{0} k_{1}^{4} e^{\left(2 \, \alpha\right)}\right)} k_{2}^{5} + 15 \, {\left(k_{1}^{9} e^{\left(2 \, \alpha\right)} + c_{1} k_{1}^{7} e^{\left(2 \, \alpha\right)} + c_{0} k_{1}^{5} e^{\left(2 \, \alpha\right)}\right)} k_{2}^{4} + 20 \, {\left(k_{1}^{10} e^{\left(2 \, \alpha\right)} + c_{1} k_{1}^{8} e^{\left(2 \, \alpha\right)} + c_{0} k_{1}^{6} e^{\left(2 \, \alpha\right)}\right)} k_{2}^{3} + 15 \, {\left(k_{1}^{11} e^{\left(2 \, \alpha\right)} + c_{1} k_{1}^{9} e^{\left(2 \, \alpha\right)} + c_{0} k_{1}^{7} e^{\left(2 \, \alpha\right)}\right)} k_{2}^{2} + 6 \, {\left(k_{1}^{12} e^{\left(2 \, \alpha\right)} + c_{1} k_{1}^{10} e^{\left(2 \, \alpha\right)} + c_{0} k_{1}^{8} e^{\left(2 \, \alpha\right)}\right)} k_{2}\right)} e^{\left(2 \, k_{1} x\right)} - {\left(6 \, k_{1} k_{2}^{12} e^{\beta} + k_{2}^{13} e^{\beta} + {\left(15 \, k_{1}^{2} e^{\beta} + c_{1} e^{\beta}\right)} k_{2}^{11} + 2 \, {\left(10 \, k_{1}^{3} e^{\beta} + 3 \, c_{1} k_{1} e^{\beta}\right)} k_{2}^{10} + c_{0} k_{1}^{6} k_{2}^{3} e^{\beta} + 6 \, c_{0} k_{1}^{5} k_{2}^{4} e^{\beta} + {\left(15 \, k_{1}^{4} e^{\beta} + 15 \, c_{1} k_{1}^{2} e^{\beta} + c_{0} e^{\beta}\right)} k_{2}^{9} + 2 \, {\left(3 \, k_{1}^{5} e^{\beta} + 10 \, c_{1} k_{1}^{3} e^{\beta} + 3 \, c_{0} k_{1} e^{\beta}\right)} k_{2}^{8} + {\left(k_{1}^{6} e^{\beta} + 15 \, c_{1} k_{1}^{4} e^{\beta} + 15 \, c_{0} k_{1}^{2} e^{\beta}\right)} k_{2}^{7} + 2 \, {\left(3 \, c_{1} k_{1}^{5} e^{\beta} + 10 \, c_{0} k_{1}^{3} e^{\beta}\right)} k_{2}^{6} + {\left(c_{1} k_{1}^{6} e^{\beta} + 15 \, c_{0} k_{1}^{4} e^{\beta}\right)} k_{2}^{5} + {\left(2 \, k_{1} k_{2}^{12} e^{\left(3 \, \alpha + \beta\right)} + k_{2}^{13} e^{\left(3 \, \alpha + \beta\right)} - {\left(k_{1}^{2} e^{\left(3 \, \alpha + \beta\right)} - c_{1} e^{\left(3 \, \alpha + \beta\right)}\right)} k_{2}^{11} - 2 \, {\left(2 \, k_{1}^{3} e^{\left(3 \, \alpha + \beta\right)} - c_{1} k_{1} e^{\left(3 \, \alpha + \beta\right)}\right)} k_{2}^{10} + c_{0} k_{1}^{6} k_{2}^{3} e^{\left(3 \, \alpha + \beta\right)} + 2 \, c_{0} k_{1}^{5} k_{2}^{4} e^{\left(3 \, \alpha + \beta\right)} - {\left(k_{1}^{4} e^{\left(3 \, \alpha + \beta\right)} + c_{1} k_{1}^{2} e^{\left(3 \, \alpha + \beta\right)} - c_{0} e^{\left(3 \, \alpha + \beta\right)}\right)} k_{2}^{9} + 2 \, {\left(k_{1}^{5} e^{\left(3 \, \alpha + \beta\right)} - 2 \, c_{1} k_{1}^{3} e^{\left(3 \, \alpha + \beta\right)} + c_{0} k_{1} e^{\left(3 \, \alpha + \beta\right)}\right)} k_{2}^{8} + {\left(k_{1}^{6} e^{\left(3 \, \alpha + \beta\right)} - c_{1} k_{1}^{4} e^{\left(3 \, \alpha + \beta\right)} - c_{0} k_{1}^{2} e^{\left(3 \, \alpha + \beta\right)}\right)} k_{2}^{7} + 2 \, {\left(c_{1} k_{1}^{5} e^{\left(3 \, \alpha + \beta\right)} - 2 \, c_{0} k_{1}^{3} e^{\left(3 \, \alpha + \beta\right)}\right)} k_{2}^{6} + {\left(c_{1} k_{1}^{6} e^{\left(3 \, \alpha + \beta\right)} - c_{0} k_{1}^{4} e^{\left(3 \, \alpha + \beta\right)}\right)} k_{2}^{5}\right)} e^{\left(3 \, k_{1} x\right)} - {\left(3 \, k_{1}^{13} e^{\left(2 \, \alpha + \beta\right)} - 10 \, k_{1} k_{2}^{12} e^{\left(2 \, \alpha + \beta\right)} - 3 \, k_{2}^{13} e^{\left(2 \, \alpha + \beta\right)} + 3 \, c_{1} k_{1}^{11} e^{\left(2 \, \alpha + \beta\right)} - {\left(5 \, k_{1}^{2} e^{\left(2 \, \alpha + \beta\right)} + 3 \, c_{1} e^{\left(2 \, \alpha + \beta\right)}\right)} k_{2}^{11} + 2 \, {\left(8 \, k_{1}^{3} e^{\left(2 \, \alpha + \beta\right)} - 5 \, c_{1} k_{1} e^{\left(2 \, \alpha + \beta\right)}\right)} k_{2}^{10} + 3 \, c_{0} k_{1}^{9} e^{\left(2 \, \alpha + \beta\right)} + {\left(19 \, k_{1}^{4} e^{\left(2 \, \alpha + \beta\right)} - 5 \, c_{1} k_{1}^{2} e^{\left(2 \, \alpha + \beta\right)} - 3 \, c_{0} e^{\left(2 \, \alpha + \beta\right)}\right)} k_{2}^{9} - 2 \, {\left(k_{1}^{5} e^{\left(2 \, \alpha + \beta\right)} - 8 \, c_{1} k_{1}^{3} e^{\left(2 \, \alpha + \beta\right)} + 5 \, c_{0} k_{1} e^{\left(2 \, \alpha + \beta\right)}\right)} k_{2}^{8} - {\left(7 \, k_{1}^{6} e^{\left(2 \, \alpha + \beta\right)} - 23 \, c_{1} k_{1}^{4} e^{\left(2 \, \alpha + \beta\right)} + c_{0} k_{1}^{2} e^{\left(2 \, \alpha + \beta\right)}\right)} k_{2}^{7} + {\left(7 \, k_{1}^{7} e^{\left(2 \, \alpha + \beta\right)} + 9 \, c_{1} k_{1}^{5} e^{\left(2 \, \alpha + \beta\right)} + 27 \, c_{0} k_{1}^{3} e^{\left(2 \, \alpha + \beta\right)}\right)} k_{2}^{6} + {\left(2 \, k_{1}^{8} e^{\left(2 \, \alpha + \beta\right)} - 9 \, c_{1} k_{1}^{6} e^{\left(2 \, \alpha + \beta\right)} + 21 \, c_{0} k_{1}^{4} e^{\left(2 \, \alpha + \beta\right)}\right)} k_{2}^{5} - {\left(19 \, k_{1}^{9} e^{\left(2 \, \alpha + \beta\right)} + 23 \, c_{1} k_{1}^{7} e^{\left(2 \, \alpha + \beta\right)} + 21 \, c_{0} k_{1}^{5} e^{\left(2 \, \alpha + \beta\right)}\right)} k_{2}^{4} - {\left(16 \, k_{1}^{10} e^{\left(2 \, \alpha + \beta\right)} + 16 \, c_{1} k_{1}^{8} e^{\left(2 \, \alpha + \beta\right)} + 27 \, c_{0} k_{1}^{6} e^{\left(2 \, \alpha + \beta\right)}\right)} k_{2}^{3} + {\left(5 \, k_{1}^{11} e^{\left(2 \, \alpha + \beta\right)} + 5 \, c_{1} k_{1}^{9} e^{\left(2 \, \alpha + \beta\right)} + c_{0} k_{1}^{7} e^{\left(2 \, \alpha + \beta\right)}\right)} k_{2}^{2} + 10 \, {\left(k_{1}^{12} e^{\left(2 \, \alpha + \beta\right)} + c_{1} k_{1}^{10} e^{\left(2 \, \alpha + \beta\right)} + c_{0} k_{1}^{8} e^{\left(2 \, \alpha + \beta\right)}\right)} k_{2}\right)} e^{\left(2 \, k_{1} x\right)} + {\left(3 \, k_{1}^{13} e^{\left(\alpha + \beta\right)} + 14 \, k_{1} k_{2}^{12} e^{\left(\alpha + \beta\right)} + 3 \, k_{2}^{13} e^{\left(\alpha + \beta\right)} + 3 \, c_{1} k_{1}^{11} e^{\left(\alpha + \beta\right)} + 14 \, c_{1} k_{1} k_{2}^{10} e^{\left(\alpha + \beta\right)} + 3 \, {\left(7 \, k_{1}^{2} e^{\left(\alpha + \beta\right)} + c_{1} e^{\left(\alpha + \beta\right)}\right)} k_{2}^{11} + 3 \, c_{0} k_{1}^{9} e^{\left(\alpha + \beta\right)} - 21 \, c_{0} k_{1}^{6} k_{2}^{3} e^{\left(\alpha + \beta\right)} - {\left(35 \, k_{1}^{4} e^{\left(\alpha + \beta\right)} - 21 \, c_{1} k_{1}^{2} e^{\left(\alpha + \beta\right)} - 3 \, c_{0} e^{\left(\alpha + \beta\right)}\right)} k_{2}^{9} - 14 \, {\left(3 \, k_{1}^{5} e^{\left(\alpha + \beta\right)} - c_{0} k_{1} e^{\left(\alpha + \beta\right)}\right)} k_{2}^{8} - {\left(25 \, k_{1}^{6} e^{\left(\alpha + \beta\right)} + 39 \, c_{1} k_{1}^{4} e^{\left(\alpha + \beta\right)} - 17 \, c_{0} k_{1}^{2} e^{\left(\alpha + \beta\right)}\right)} k_{2}^{7} - {\left(25 \, k_{1}^{7} e^{\left(\alpha + \beta\right)} + 63 \, c_{1} k_{1}^{5} e^{\left(\alpha + \beta\right)} + 21 \, c_{0} k_{1}^{3} e^{\left(\alpha + \beta\right)}\right)} k_{2}^{6} - 7 \, {\left(6 \, k_{1}^{8} e^{\left(\alpha + \beta\right)} + 9 \, c_{1} k_{1}^{6} e^{\left(\alpha + \beta\right)} + 11 \, c_{0} k_{1}^{4} e^{\left(\alpha + \beta\right)}\right)} k_{2}^{5} - {\left(35 \, k_{1}^{9} e^{\left(\alpha + \beta\right)} + 39 \, c_{1} k_{1}^{7} e^{\left(\alpha + \beta\right)} + 77 \, c_{0} k_{1}^{5} e^{\left(\alpha + \beta\right)}\right)} k_{2}^{4} + {\left(21 \, k_{1}^{11} e^{\left(\alpha + \beta\right)} + 21 \, c_{1} k_{1}^{9} e^{\left(\alpha + \beta\right)} + 17 \, c_{0} k_{1}^{7} e^{\left(\alpha + \beta\right)}\right)} k_{2}^{2} + 14 \, {\left(k_{1}^{12} e^{\left(\alpha + \beta\right)} + c_{1} k_{1}^{10} e^{\left(\alpha + \beta\right)} + c_{0} k_{1}^{8} e^{\left(\alpha + \beta\right)}\right)} k_{2}\right)} e^{\left(k_{1} x\right)}\right)} e^{\left(k_{2} x\right)} + {\left(6 \, k_{1} k_{2}^{12} e^{\left(2 \, \beta\right)} + k_{2}^{13} e^{\left(2 \, \beta\right)} + {\left(15 \, k_{1}^{2} e^{\left(2 \, \beta\right)} + c_{1} e^{\left(2 \, \beta\right)}\right)} k_{2}^{11} + 2 \, {\left(10 \, k_{1}^{3} e^{\left(2 \, \beta\right)} + 3 \, c_{1} k_{1} e^{\left(2 \, \beta\right)}\right)} k_{2}^{10} + c_{0} k_{1}^{6} k_{2}^{3} e^{\left(2 \, \beta\right)} + 6 \, c_{0} k_{1}^{5} k_{2}^{4} e^{\left(2 \, \beta\right)} + {\left(15 \, k_{1}^{4} e^{\left(2 \, \beta\right)} + 15 \, c_{1} k_{1}^{2} e^{\left(2 \, \beta\right)} + c_{0} e^{\left(2 \, \beta\right)}\right)} k_{2}^{9} + 2 \, {\left(3 \, k_{1}^{5} e^{\left(2 \, \beta\right)} + 10 \, c_{1} k_{1}^{3} e^{\left(2 \, \beta\right)} + 3 \, c_{0} k_{1} e^{\left(2 \, \beta\right)}\right)} k_{2}^{8} + {\left(k_{1}^{6} e^{\left(2 \, \beta\right)} + 15 \, c_{1} k_{1}^{4} e^{\left(2 \, \beta\right)} + 15 \, c_{0} k_{1}^{2} e^{\left(2 \, \beta\right)}\right)} k_{2}^{7} + 2 \, {\left(3 \, c_{1} k_{1}^{5} e^{\left(2 \, \beta\right)} + 10 \, c_{0} k_{1}^{3} e^{\left(2 \, \beta\right)}\right)} k_{2}^{6} + {\left(c_{1} k_{1}^{6} e^{\left(2 \, \beta\right)} + 15 \, c_{0} k_{1}^{4} e^{\left(2 \, \beta\right)}\right)} k_{2}^{5} - {\left(2 \, k_{1} k_{2}^{12} e^{\left(3 \, \alpha + 2 \, \beta\right)} - k_{2}^{13} e^{\left(3 \, \alpha + 2 \, \beta\right)} + {\left(k_{1}^{2} e^{\left(3 \, \alpha + 2 \, \beta\right)} - c_{1} e^{\left(3 \, \alpha + 2 \, \beta\right)}\right)} k_{2}^{11} - 2 \, {\left(2 \, k_{1}^{3} e^{\left(3 \, \alpha + 2 \, \beta\right)} - c_{1} k_{1} e^{\left(3 \, \alpha + 2 \, \beta\right)}\right)} k_{2}^{10} - c_{0} k_{1}^{6} k_{2}^{3} e^{\left(3 \, \alpha + 2 \, \beta\right)} + 2 \, c_{0} k_{1}^{5} k_{2}^{4} e^{\left(3 \, \alpha + 2 \, \beta\right)} + {\left(k_{1}^{4} e^{\left(3 \, \alpha + 2 \, \beta\right)} + c_{1} k_{1}^{2} e^{\left(3 \, \alpha + 2 \, \beta\right)} - c_{0} e^{\left(3 \, \alpha + 2 \, \beta\right)}\right)} k_{2}^{9} + 2 \, {\left(k_{1}^{5} e^{\left(3 \, \alpha + 2 \, \beta\right)} - 2 \, c_{1} k_{1}^{3} e^{\left(3 \, \alpha + 2 \, \beta\right)} + c_{0} k_{1} e^{\left(3 \, \alpha + 2 \, \beta\right)}\right)} k_{2}^{8} - {\left(k_{1}^{6} e^{\left(3 \, \alpha + 2 \, \beta\right)} - c_{1} k_{1}^{4} e^{\left(3 \, \alpha + 2 \, \beta\right)} - c_{0} k_{1}^{2} e^{\left(3 \, \alpha + 2 \, \beta\right)}\right)} k_{2}^{7} + 2 \, {\left(c_{1} k_{1}^{5} e^{\left(3 \, \alpha + 2 \, \beta\right)} - 2 \, c_{0} k_{1}^{3} e^{\left(3 \, \alpha + 2 \, \beta\right)}\right)} k_{2}^{6} - {\left(c_{1} k_{1}^{6} e^{\left(3 \, \alpha + 2 \, \beta\right)} - c_{0} k_{1}^{4} e^{\left(3 \, \alpha + 2 \, \beta\right)}\right)} k_{2}^{5}\right)} e^{\left(3 \, k_{1} x\right)} + {\left(3 \, k_{1}^{13} e^{\left(2 \, \alpha + 2 \, \beta\right)} + 2 \, k_{1} k_{2}^{12} e^{\left(2 \, \alpha + 2 \, \beta\right)} + 3 \, k_{2}^{13} e^{\left(2 \, \alpha + 2 \, \beta\right)} + 3 \, c_{1} k_{1}^{11} e^{\left(2 \, \alpha + 2 \, \beta\right)} - {\left(11 \, k_{1}^{2} e^{\left(2 \, \alpha + 2 \, \beta\right)} - 3 \, c_{1} e^{\left(2 \, \alpha + 2 \, \beta\right)}\right)} k_{2}^{11} - 2 \, {\left(4 \, k_{1}^{3} e^{\left(2 \, \alpha + 2 \, \beta\right)} - c_{1} k_{1} e^{\left(2 \, \alpha + 2 \, \beta\right)}\right)} k_{2}^{10} + 3 \, c_{0} k_{1}^{9} e^{\left(2 \, \alpha + 2 \, \beta\right)} + {\left(13 \, k_{1}^{4} e^{\left(2 \, \alpha + 2 \, \beta\right)} - 11 \, c_{1} k_{1}^{2} e^{\left(2 \, \alpha + 2 \, \beta\right)} + 3 \, c_{0} e^{\left(2 \, \alpha + 2 \, \beta\right)}\right)} k_{2}^{9} + 2 \, {\left(5 \, k_{1}^{5} e^{\left(2 \, \alpha + 2 \, \beta\right)} - 4 \, c_{1} k_{1}^{3} e^{\left(2 \, \alpha + 2 \, \beta\right)} + c_{0} k_{1} e^{\left(2 \, \alpha + 2 \, \beta\right)}\right)} k_{2}^{8} - 3 \, {\left(3 \, k_{1}^{6} e^{\left(2 \, \alpha + 2 \, \beta\right)} - 3 \, c_{1} k_{1}^{4} e^{\left(2 \, \alpha + 2 \, \beta\right)} + 5 \, c_{0} k_{1}^{2} e^{\left(2 \, \alpha + 2 \, \beta\right)}\right)} k_{2}^{7} - {\left(9 \, k_{1}^{7} e^{\left(2 \, \alpha + 2 \, \beta\right)} - 5 \, c_{1} k_{1}^{5} e^{\left(2 \, \alpha + 2 \, \beta\right)} + 13 \, c_{0} k_{1}^{3} e^{\left(2 \, \alpha + 2 \, \beta\right)}\right)} k_{2}^{6} + {\left(10 \, k_{1}^{8} e^{\left(2 \, \alpha + 2 \, \beta\right)} + 5 \, c_{1} k_{1}^{6} e^{\left(2 \, \alpha + 2 \, \beta\right)} + 23 \, c_{0} k_{1}^{4} e^{\left(2 \, \alpha + 2 \, \beta\right)}\right)} k_{2}^{5} + {\left(13 \, k_{1}^{9} e^{\left(2 \, \alpha + 2 \, \beta\right)} + 9 \, c_{1} k_{1}^{7} e^{\left(2 \, \alpha + 2 \, \beta\right)} + 23 \, c_{0} k_{1}^{5} e^{\left(2 \, \alpha + 2 \, \beta\right)}\right)} k_{2}^{4} - {\left(8 \, k_{1}^{10} e^{\left(2 \, \alpha + 2 \, \beta\right)} + 8 \, c_{1} k_{1}^{8} e^{\left(2 \, \alpha + 2 \, \beta\right)} + 13 \, c_{0} k_{1}^{6} e^{\left(2 \, \alpha + 2 \, \beta\right)}\right)} k_{2}^{3} - {\left(11 \, k_{1}^{11} e^{\left(2 \, \alpha + 2 \, \beta\right)} + 11 \, c_{1} k_{1}^{9} e^{\left(2 \, \alpha + 2 \, \beta\right)} + 15 \, c_{0} k_{1}^{7} e^{\left(2 \, \alpha + 2 \, \beta\right)}\right)} k_{2}^{2} + 2 \, {\left(k_{1}^{12} e^{\left(2 \, \alpha + 2 \, \beta\right)} + c_{1} k_{1}^{10} e^{\left(2 \, \alpha + 2 \, \beta\right)} + c_{0} k_{1}^{8} e^{\left(2 \, \alpha + 2 \, \beta\right)}\right)} k_{2}\right)} e^{\left(2 \, k_{1} x\right)} - {\left(3 \, k_{1}^{13} e^{\left(\alpha + 2 \, \beta\right)} - 10 \, k_{1} k_{2}^{12} e^{\left(\alpha + 2 \, \beta\right)} - 3 \, k_{2}^{13} e^{\left(\alpha + 2 \, \beta\right)} + 3 \, c_{1} k_{1}^{11} e^{\left(\alpha + 2 \, \beta\right)} - {\left(5 \, k_{1}^{2} e^{\left(\alpha + 2 \, \beta\right)} + 3 \, c_{1} e^{\left(\alpha + 2 \, \beta\right)}\right)} k_{2}^{11} + 2 \, {\left(8 \, k_{1}^{3} e^{\left(\alpha + 2 \, \beta\right)} - 5 \, c_{1} k_{1} e^{\left(\alpha + 2 \, \beta\right)}\right)} k_{2}^{10} + 3 \, c_{0} k_{1}^{9} e^{\left(\alpha + 2 \, \beta\right)} + {\left(19 \, k_{1}^{4} e^{\left(\alpha + 2 \, \beta\right)} - 5 \, c_{1} k_{1}^{2} e^{\left(\alpha + 2 \, \beta\right)} - 3 \, c_{0} e^{\left(\alpha + 2 \, \beta\right)}\right)} k_{2}^{9} - 2 \, {\left(k_{1}^{5} e^{\left(\alpha + 2 \, \beta\right)} - 8 \, c_{1} k_{1}^{3} e^{\left(\alpha + 2 \, \beta\right)} + 5 \, c_{0} k_{1} e^{\left(\alpha + 2 \, \beta\right)}\right)} k_{2}^{8} - {\left(7 \, k_{1}^{6} e^{\left(\alpha + 2 \, \beta\right)} - 23 \, c_{1} k_{1}^{4} e^{\left(\alpha + 2 \, \beta\right)} + c_{0} k_{1}^{2} e^{\left(\alpha + 2 \, \beta\right)}\right)} k_{2}^{7} + {\left(7 \, k_{1}^{7} e^{\left(\alpha + 2 \, \beta\right)} + 9 \, c_{1} k_{1}^{5} e^{\left(\alpha + 2 \, \beta\right)} + 27 \, c_{0} k_{1}^{3} e^{\left(\alpha + 2 \, \beta\right)}\right)} k_{2}^{6} + {\left(2 \, k_{1}^{8} e^{\left(\alpha + 2 \, \beta\right)} - 9 \, c_{1} k_{1}^{6} e^{\left(\alpha + 2 \, \beta\right)} + 21 \, c_{0} k_{1}^{4} e^{\left(\alpha + 2 \, \beta\right)}\right)} k_{2}^{5} - {\left(19 \, k_{1}^{9} e^{\left(\alpha + 2 \, \beta\right)} + 23 \, c_{1} k_{1}^{7} e^{\left(\alpha + 2 \, \beta\right)} + 21 \, c_{0} k_{1}^{5} e^{\left(\alpha + 2 \, \beta\right)}\right)} k_{2}^{4} - {\left(16 \, k_{1}^{10} e^{\left(\alpha + 2 \, \beta\right)} + 16 \, c_{1} k_{1}^{8} e^{\left(\alpha + 2 \, \beta\right)} + 27 \, c_{0} k_{1}^{6} e^{\left(\alpha + 2 \, \beta\right)}\right)} k_{2}^{3} + {\left(5 \, k_{1}^{11} e^{\left(\alpha + 2 \, \beta\right)} + 5 \, c_{1} k_{1}^{9} e^{\left(\alpha + 2 \, \beta\right)} + c_{0} k_{1}^{7} e^{\left(\alpha + 2 \, \beta\right)}\right)} k_{2}^{2} + 10 \, {\left(k_{1}^{12} e^{\left(\alpha + 2 \, \beta\right)} + c_{1} k_{1}^{10} e^{\left(\alpha + 2 \, \beta\right)} + c_{0} k_{1}^{8} e^{\left(\alpha + 2 \, \beta\right)}\right)} k_{2}\right)} e^{\left(k_{1} x\right)}\right)} e^{\left(2 \, k_{2} x\right)}\right)}}{k_{1}^{6} + 6 \, k_{1}^{5} k_{2} + 15 \, k_{1}^{4} k_{2}^{2} + 20 \, k_{1}^{3} k_{2}^{3} + 15 \, k_{1}^{2} k_{2}^{4} + 6 \, k_{1} k_{2}^{5} + k_{2}^{6} + 3 \, {\left(k_{1}^{6} e^{\alpha} + 6 \, k_{1}^{5} k_{2} e^{\alpha} + 15 \, k_{1}^{4} k_{2}^{2} e^{\alpha} + 20 \, k_{1}^{3} k_{2}^{3} e^{\alpha} + 15 \, k_{1}^{2} k_{2}^{4} e^{\alpha} + 6 \, k_{1} k_{2}^{5} e^{\alpha} + k_{2}^{6} e^{\alpha}\right)} e^{\left(k_{1} x\right)} + {\left(k_{1}^{6} e^{\left(3 \, \alpha\right)} + 6 \, k_{1}^{5} k_{2} e^{\left(3 \, \alpha\right)} + 15 \, k_{1}^{4} k_{2}^{2} e^{\left(3 \, \alpha\right)} + 20 \, k_{1}^{3} k_{2}^{3} e^{\left(3 \, \alpha\right)} + 15 \, k_{1}^{2} k_{2}^{4} e^{\left(3 \, \alpha\right)} + 6 \, k_{1} k_{2}^{5} e^{\left(3 \, \alpha\right)} + k_{2}^{6} e^{\left(3 \, \alpha\right)}\right)} e^{\left(3 \, k_{1} x\right)} + 3 \, {\left(k_{1}^{6} e^{\left(2 \, \alpha\right)} + 6 \, k_{1}^{5} k_{2} e^{\left(2 \, \alpha\right)} + 15 \, k_{1}^{4} k_{2}^{2} e^{\left(2 \, \alpha\right)} + 20 \, k_{1}^{3} k_{2}^{3} e^{\left(2 \, \alpha\right)} + 15 \, k_{1}^{2} k_{2}^{4} e^{\left(2 \, \alpha\right)} + 6 \, k_{1} k_{2}^{5} e^{\left(2 \, \alpha\right)} + k_{2}^{6} e^{\left(2 \, \alpha\right)}\right)} e^{\left(2 \, k_{1} x\right)} + 3 \, {\left(k_{1}^{6} e^{\beta} + 6 \, k_{1}^{5} k_{2} e^{\beta} + 15 \, k_{1}^{4} k_{2}^{2} e^{\beta} + 20 \, k_{1}^{3} k_{2}^{3} e^{\beta} + 15 \, k_{1}^{2} k_{2}^{4} e^{\beta} + 6 \, k_{1} k_{2}^{5} e^{\beta} + k_{2}^{6} e^{\beta} + {\left(k_{1}^{6} e^{\left(3 \, \alpha + \beta\right)} + 2 \, k_{1}^{5} k_{2} e^{\left(3 \, \alpha + \beta\right)} - k_{1}^{4} k_{2}^{2} e^{\left(3 \, \alpha + \beta\right)} - 4 \, k_{1}^{3} k_{2}^{3} e^{\left(3 \, \alpha + \beta\right)} - k_{1}^{2} k_{2}^{4} e^{\left(3 \, \alpha + \beta\right)} + 2 \, k_{1} k_{2}^{5} e^{\left(3 \, \alpha + \beta\right)} + k_{2}^{6} e^{\left(3 \, \alpha + \beta\right)}\right)} e^{\left(3 \, k_{1} x\right)} + {\left(3 \, k_{1}^{6} e^{\left(2 \, \alpha + \beta\right)} + 10 \, k_{1}^{5} k_{2} e^{\left(2 \, \alpha + \beta\right)} + 13 \, k_{1}^{4} k_{2}^{2} e^{\left(2 \, \alpha + \beta\right)} + 12 \, k_{1}^{3} k_{2}^{3} e^{\left(2 \, \alpha + \beta\right)} + 13 \, k_{1}^{2} k_{2}^{4} e^{\left(2 \, \alpha + \beta\right)} + 10 \, k_{1} k_{2}^{5} e^{\left(2 \, \alpha + \beta\right)} + 3 \, k_{2}^{6} e^{\left(2 \, \alpha + \beta\right)}\right)} e^{\left(2 \, k_{1} x\right)} + {\left(3 \, k_{1}^{6} e^{\left(\alpha + \beta\right)} + 14 \, k_{1}^{5} k_{2} e^{\left(\alpha + \beta\right)} + 29 \, k_{1}^{4} k_{2}^{2} e^{\left(\alpha + \beta\right)} + 36 \, k_{1}^{3} k_{2}^{3} e^{\left(\alpha + \beta\right)} + 29 \, k_{1}^{2} k_{2}^{4} e^{\left(\alpha + \beta\right)} + 14 \, k_{1} k_{2}^{5} e^{\left(\alpha + \beta\right)} + 3 \, k_{2}^{6} e^{\left(\alpha + \beta\right)}\right)} e^{\left(k_{1} x\right)}\right)} e^{\left(k_{2} x\right)} + {\left(k_{1}^{6} e^{\left(3 \, \beta\right)} + 6 \, k_{1}^{5} k_{2} e^{\left(3 \, \beta\right)} + 15 \, k_{1}^{4} k_{2}^{2} e^{\left(3 \, \beta\right)} + 20 \, k_{1}^{3} k_{2}^{3} e^{\left(3 \, \beta\right)} + 15 \, k_{1}^{2} k_{2}^{4} e^{\left(3 \, \beta\right)} + 6 \, k_{1} k_{2}^{5} e^{\left(3 \, \beta\right)} + k_{2}^{6} e^{\left(3 \, \beta\right)} + {\left(k_{1}^{6} e^{\left(3 \, \alpha + 3 \, \beta\right)} - 6 \, k_{1}^{5} k_{2} e^{\left(3 \, \alpha + 3 \, \beta\right)} + 15 \, k_{1}^{4} k_{2}^{2} e^{\left(3 \, \alpha + 3 \, \beta\right)} - 20 \, k_{1}^{3} k_{2}^{3} e^{\left(3 \, \alpha + 3 \, \beta\right)} + 15 \, k_{1}^{2} k_{2}^{4} e^{\left(3 \, \alpha + 3 \, \beta\right)} - 6 \, k_{1} k_{2}^{5} e^{\left(3 \, \alpha + 3 \, \beta\right)} + k_{2}^{6} e^{\left(3 \, \alpha + 3 \, \beta\right)}\right)} e^{\left(3 \, k_{1} x\right)} + 3 \, {\left(k_{1}^{6} e^{\left(2 \, \alpha + 3 \, \beta\right)} - 2 \, k_{1}^{5} k_{2} e^{\left(2 \, \alpha + 3 \, \beta\right)} - k_{1}^{4} k_{2}^{2} e^{\left(2 \, \alpha + 3 \, \beta\right)} + 4 \, k_{1}^{3} k_{2}^{3} e^{\left(2 \, \alpha + 3 \, \beta\right)} - k_{1}^{2} k_{2}^{4} e^{\left(2 \, \alpha + 3 \, \beta\right)} - 2 \, k_{1} k_{2}^{5} e^{\left(2 \, \alpha + 3 \, \beta\right)} + k_{2}^{6} e^{\left(2 \, \alpha + 3 \, \beta\right)}\right)} e^{\left(2 \, k_{1} x\right)} + 3 \, {\left(k_{1}^{6} e^{\left(\alpha + 3 \, \beta\right)} + 2 \, k_{1}^{5} k_{2} e^{\left(\alpha + 3 \, \beta\right)} - k_{1}^{4} k_{2}^{2} e^{\left(\alpha + 3 \, \beta\right)} - 4 \, k_{1}^{3} k_{2}^{3} e^{\left(\alpha + 3 \, \beta\right)} - k_{1}^{2} k_{2}^{4} e^{\left(\alpha + 3 \, \beta\right)} + 2 \, k_{1} k_{2}^{5} e^{\left(\alpha + 3 \, \beta\right)} + k_{2}^{6} e^{\left(\alpha + 3 \, \beta\right)}\right)} e^{\left(k_{1} x\right)}\right)} e^{\left(3 \, k_{2} x\right)} + 3 \, {\left(k_{1}^{6} e^{\left(2 \, \beta\right)} + 6 \, k_{1}^{5} k_{2} e^{\left(2 \, \beta\right)} + 15 \, k_{1}^{4} k_{2}^{2} e^{\left(2 \, \beta\right)} + 20 \, k_{1}^{3} k_{2}^{3} e^{\left(2 \, \beta\right)} + 15 \, k_{1}^{2} k_{2}^{4} e^{\left(2 \, \beta\right)} + 6 \, k_{1} k_{2}^{5} e^{\left(2 \, \beta\right)} + k_{2}^{6} e^{\left(2 \, \beta\right)} + {\left(k_{1}^{6} e^{\left(3 \, \alpha + 2 \, \beta\right)} - 2 \, k_{1}^{5} k_{2} e^{\left(3 \, \alpha + 2 \, \beta\right)} - k_{1}^{4} k_{2}^{2} e^{\left(3 \, \alpha + 2 \, \beta\right)} + 4 \, k_{1}^{3} k_{2}^{3} e^{\left(3 \, \alpha + 2 \, \beta\right)} - k_{1}^{2} k_{2}^{4} e^{\left(3 \, \alpha + 2 \, \beta\right)} - 2 \, k_{1} k_{2}^{5} e^{\left(3 \, \alpha + 2 \, \beta\right)} + k_{2}^{6} e^{\left(3 \, \alpha + 2 \, \beta\right)}\right)} e^{\left(3 \, k_{1} x\right)} + {\left(3 \, k_{1}^{6} e^{\left(2 \, \alpha + 2 \, \beta\right)} + 2 \, k_{1}^{5} k_{2} e^{\left(2 \, \alpha + 2 \, \beta\right)} - 3 \, k_{1}^{4} k_{2}^{2} e^{\left(2 \, \alpha + 2 \, \beta\right)} - 4 \, k_{1}^{3} k_{2}^{3} e^{\left(2 \, \alpha + 2 \, \beta\right)} - 3 \, k_{1}^{2} k_{2}^{4} e^{\left(2 \, \alpha + 2 \, \beta\right)} + 2 \, k_{1} k_{2}^{5} e^{\left(2 \, \alpha + 2 \, \beta\right)} + 3 \, k_{2}^{6} e^{\left(2 \, \alpha + 2 \, \beta\right)}\right)} e^{\left(2 \, k_{1} x\right)} + {\left(3 \, k_{1}^{6} e^{\left(\alpha + 2 \, \beta\right)} + 10 \, k_{1}^{5} k_{2} e^{\left(\alpha + 2 \, \beta\right)} + 13 \, k_{1}^{4} k_{2}^{2} e^{\left(\alpha + 2 \, \beta\right)} + 12 \, k_{1}^{3} k_{2}^{3} e^{\left(\alpha + 2 \, \beta\right)} + 13 \, k_{1}^{2} k_{2}^{4} e^{\left(\alpha + 2 \, \beta\right)} + 10 \, k_{1} k_{2}^{5} e^{\left(\alpha + 2 \, \beta\right)} + 3 \, k_{2}^{6} e^{\left(\alpha + 2 \, \beta\right)}\right)} e^{\left(k_{1} x\right)}\right)} e^{\left(2 \, k_{2} x\right)}}

\newcommand{\Bold}[1]{\mathbf{#1}}-\frac{2 \, {\left({\left({\left(k_{1}^{13} e^{\left(2 \, \alpha + 3 \, \beta\right)} + c_{1} k_{1}^{11} e^{\left(2 \, \alpha + 3 \, \beta\right)} + c_{0} k_{1}^{9} e^{\left(2 \, \alpha + 3 \, \beta\right)} + {\left(k_{1}^{7} e^{\left(2 \, \alpha + 3 \, \beta\right)} + c_{1} k_{1}^{5} e^{\left(2 \, \alpha + 3 \, \beta\right)} + c_{0} k_{1}^{3} e^{\left(2 \, \alpha + 3 \, \beta\right)}\right)} k_{2}^{6} - 2 \, {\left(k_{1}^{8} e^{\left(2 \, \alpha + 3 \, \beta\right)} + c_{1} k_{1}^{6} e^{\left(2 \, \alpha + 3 \, \beta\right)} + c_{0} k_{1}^{4} e^{\left(2 \, \alpha + 3 \, \beta\right)}\right)} k_{2}^{5} - {\left(k_{1}^{9} e^{\left(2 \, \alpha + 3 \, \beta\right)} + c_{1} k_{1}^{7} e^{\left(2 \, \alpha + 3 \, \beta\right)} + c_{0} k_{1}^{5} e^{\left(2 \, \alpha + 3 \, \beta\right)}\right)} k_{2}^{4} + 4 \, {\left(k_{1}^{10} e^{\left(2 \, \alpha + 3 \, \beta\right)} + c_{1} k_{1}^{8} e^{\left(2 \, \alpha + 3 \, \beta\right)} + c_{0} k_{1}^{6} e^{\left(2 \, \alpha + 3 \, \beta\right)}\right)} k_{2}^{3} - {\left(k_{1}^{11} e^{\left(2 \, \alpha + 3 \, \beta\right)} + c_{1} k_{1}^{9} e^{\left(2 \, \alpha + 3 \, \beta\right)} + c_{0} k_{1}^{7} e^{\left(2 \, \alpha + 3 \, \beta\right)}\right)} k_{2}^{2} - 2 \, {\left(k_{1}^{12} e^{\left(2 \, \alpha + 3 \, \beta\right)} + c_{1} k_{1}^{10} e^{\left(2 \, \alpha + 3 \, \beta\right)} + c_{0} k_{1}^{8} e^{\left(2 \, \alpha + 3 \, \beta\right)}\right)} k_{2}\right)} e^{\left(2 \, k_{1} x\right)} - {\left(k_{1}^{13} e^{\left(\alpha + 3 \, \beta\right)} + c_{1} k_{1}^{11} e^{\left(\alpha + 3 \, \beta\right)} + c_{0} k_{1}^{9} e^{\left(\alpha + 3 \, \beta\right)} + {\left(k_{1}^{7} e^{\left(\alpha + 3 \, \beta\right)} + c_{1} k_{1}^{5} e^{\left(\alpha + 3 \, \beta\right)} + c_{0} k_{1}^{3} e^{\left(\alpha + 3 \, \beta\right)}\right)} k_{2}^{6} + 2 \, {\left(k_{1}^{8} e^{\left(\alpha + 3 \, \beta\right)} + c_{1} k_{1}^{6} e^{\left(\alpha + 3 \, \beta\right)} + c_{0} k_{1}^{4} e^{\left(\alpha + 3 \, \beta\right)}\right)} k_{2}^{5} - {\left(k_{1}^{9} e^{\left(\alpha + 3 \, \beta\right)} + c_{1} k_{1}^{7} e^{\left(\alpha + 3 \, \beta\right)} + c_{0} k_{1}^{5} e^{\left(\alpha + 3 \, \beta\right)}\right)} k_{2}^{4} - 4 \, {\left(k_{1}^{10} e^{\left(\alpha + 3 \, \beta\right)} + c_{1} k_{1}^{8} e^{\left(\alpha + 3 \, \beta\right)} + c_{0} k_{1}^{6} e^{\left(\alpha + 3 \, \beta\right)}\right)} k_{2}^{3} - {\left(k_{1}^{11} e^{\left(\alpha + 3 \, \beta\right)} + c_{1} k_{1}^{9} e^{\left(\alpha + 3 \, \beta\right)} + c_{0} k_{1}^{7} e^{\left(\alpha + 3 \, \beta\right)}\right)} k_{2}^{2} + 2 \, {\left(k_{1}^{12} e^{\left(\alpha + 3 \, \beta\right)} + c_{1} k_{1}^{10} e^{\left(\alpha + 3 \, \beta\right)} + c_{0} k_{1}^{8} e^{\left(\alpha + 3 \, \beta\right)}\right)} k_{2}\right)} e^{\left(k_{1} x\right)}\right)} e^{\left(3 \, k_{2} x\right)} - {\left(k_{1}^{13} e^{\alpha} + c_{1} k_{1}^{11} e^{\alpha} + c_{0} k_{1}^{9} e^{\alpha} + {\left(k_{1}^{7} e^{\alpha} + c_{1} k_{1}^{5} e^{\alpha} + c_{0} k_{1}^{3} e^{\alpha}\right)} k_{2}^{6} + 6 \, {\left(k_{1}^{8} e^{\alpha} + c_{1} k_{1}^{6} e^{\alpha} + c_{0} k_{1}^{4} e^{\alpha}\right)} k_{2}^{5} + 15 \, {\left(k_{1}^{9} e^{\alpha} + c_{1} k_{1}^{7} e^{\alpha} + c_{0} k_{1}^{5} e^{\alpha}\right)} k_{2}^{4} + 20 \, {\left(k_{1}^{10} e^{\alpha} + c_{1} k_{1}^{8} e^{\alpha} + c_{0} k_{1}^{6} e^{\alpha}\right)} k_{2}^{3} + 15 \, {\left(k_{1}^{11} e^{\alpha} + c_{1} k_{1}^{9} e^{\alpha} + c_{0} k_{1}^{7} e^{\alpha}\right)} k_{2}^{2} + 6 \, {\left(k_{1}^{12} e^{\alpha} + c_{1} k_{1}^{10} e^{\alpha} + c_{0} k_{1}^{8} e^{\alpha}\right)} k_{2}\right)} e^{\left(k_{1} x\right)} + {\left(k_{1}^{13} e^{\left(2 \, \alpha\right)} + c_{1} k_{1}^{11} e^{\left(2 \, \alpha\right)} + c_{0} k_{1}^{9} e^{\left(2 \, \alpha\right)} + {\left(k_{1}^{7} e^{\left(2 \, \alpha\right)} + c_{1} k_{1}^{5} e^{\left(2 \, \alpha\right)} + c_{0} k_{1}^{3} e^{\left(2 \, \alpha\right)}\right)} k_{2}^{6} + 6 \, {\left(k_{1}^{8} e^{\left(2 \, \alpha\right)} + c_{1} k_{1}^{6} e^{\left(2 \, \alpha\right)} + c_{0} k_{1}^{4} e^{\left(2 \, \alpha\right)}\right)} k_{2}^{5} + 15 \, {\left(k_{1}^{9} e^{\left(2 \, \alpha\right)} + c_{1} k_{1}^{7} e^{\left(2 \, \alpha\right)} + c_{0} k_{1}^{5} e^{\left(2 \, \alpha\right)}\right)} k_{2}^{4} + 20 \, {\left(k_{1}^{10} e^{\left(2 \, \alpha\right)} + c_{1} k_{1}^{8} e^{\left(2 \, \alpha\right)} + c_{0} k_{1}^{6} e^{\left(2 \, \alpha\right)}\right)} k_{2}^{3} + 15 \, {\left(k_{1}^{11} e^{\left(2 \, \alpha\right)} + c_{1} k_{1}^{9} e^{\left(2 \, \alpha\right)} + c_{0} k_{1}^{7} e^{\left(2 \, \alpha\right)}\right)} k_{2}^{2} + 6 \, {\left(k_{1}^{12} e^{\left(2 \, \alpha\right)} + c_{1} k_{1}^{10} e^{\left(2 \, \alpha\right)} + c_{0} k_{1}^{8} e^{\left(2 \, \alpha\right)}\right)} k_{2}\right)} e^{\left(2 \, k_{1} x\right)} - {\left(6 \, k_{1} k_{2}^{12} e^{\beta} + k_{2}^{13} e^{\beta} + {\left(15 \, k_{1}^{2} e^{\beta} + c_{1} e^{\beta}\right)} k_{2}^{11} + 2 \, {\left(10 \, k_{1}^{3} e^{\beta} + 3 \, c_{1} k_{1} e^{\beta}\right)} k_{2}^{10} + c_{0} k_{1}^{6} k_{2}^{3} e^{\beta} + 6 \, c_{0} k_{1}^{5} k_{2}^{4} e^{\beta} + {\left(15 \, k_{1}^{4} e^{\beta} + 15 \, c_{1} k_{1}^{2} e^{\beta} + c_{0} e^{\beta}\right)} k_{2}^{9} + 2 \, {\left(3 \, k_{1}^{5} e^{\beta} + 10 \, c_{1} k_{1}^{3} e^{\beta} + 3 \, c_{0} k_{1} e^{\beta}\right)} k_{2}^{8} + {\left(k_{1}^{6} e^{\beta} + 15 \, c_{1} k_{1}^{4} e^{\beta} + 15 \, c_{0} k_{1}^{2} e^{\beta}\right)} k_{2}^{7} + 2 \, {\left(3 \, c_{1} k_{1}^{5} e^{\beta} + 10 \, c_{0} k_{1}^{3} e^{\beta}\right)} k_{2}^{6} + {\left(c_{1} k_{1}^{6} e^{\beta} + 15 \, c_{0} k_{1}^{4} e^{\beta}\right)} k_{2}^{5} + {\left(2 \, k_{1} k_{2}^{12} e^{\left(3 \, \alpha + \beta\right)} + k_{2}^{13} e^{\left(3 \, \alpha + \beta\right)} - {\left(k_{1}^{2} e^{\left(3 \, \alpha + \beta\right)} - c_{1} e^{\left(3 \, \alpha + \beta\right)}\right)} k_{2}^{11} - 2 \, {\left(2 \, k_{1}^{3} e^{\left(3 \, \alpha + \beta\right)} - c_{1} k_{1} e^{\left(3 \, \alpha + \beta\right)}\right)} k_{2}^{10} + c_{0} k_{1}^{6} k_{2}^{3} e^{\left(3 \, \alpha + \beta\right)} + 2 \, c_{0} k_{1}^{5} k_{2}^{4} e^{\left(3 \, \alpha + \beta\right)} - {\left(k_{1}^{4} e^{\left(3 \, \alpha + \beta\right)} + c_{1} k_{1}^{2} e^{\left(3 \, \alpha + \beta\right)} - c_{0} e^{\left(3 \, \alpha + \beta\right)}\right)} k_{2}^{9} + 2 \, {\left(k_{1}^{5} e^{\left(3 \, \alpha + \beta\right)} - 2 \, c_{1} k_{1}^{3} e^{\left(3 \, \alpha + \beta\right)} + c_{0} k_{1} e^{\left(3 \, \alpha + \beta\right)}\right)} k_{2}^{8} + {\left(k_{1}^{6} e^{\left(3 \, \alpha + \beta\right)} - c_{1} k_{1}^{4} e^{\left(3 \, \alpha + \beta\right)} - c_{0} k_{1}^{2} e^{\left(3 \, \alpha + \beta\right)}\right)} k_{2}^{7} + 2 \, {\left(c_{1} k_{1}^{5} e^{\left(3 \, \alpha + \beta\right)} - 2 \, c_{0} k_{1}^{3} e^{\left(3 \, \alpha + \beta\right)}\right)} k_{2}^{6} + {\left(c_{1} k_{1}^{6} e^{\left(3 \, \alpha + \beta\right)} - c_{0} k_{1}^{4} e^{\left(3 \, \alpha + \beta\right)}\right)} k_{2}^{5}\right)} e^{\left(3 \, k_{1} x\right)} - {\left(3 \, k_{1}^{13} e^{\left(2 \, \alpha + \beta\right)} - 10 \, k_{1} k_{2}^{12} e^{\left(2 \, \alpha + \beta\right)} - 3 \, k_{2}^{13} e^{\left(2 \, \alpha + \beta\right)} + 3 \, c_{1} k_{1}^{11} e^{\left(2 \, \alpha + \beta\right)} - {\left(5 \, k_{1}^{2} e^{\left(2 \, \alpha + \beta\right)} + 3 \, c_{1} e^{\left(2 \, \alpha + \beta\right)}\right)} k_{2}^{11} + 2 \, {\left(8 \, k_{1}^{3} e^{\left(2 \, \alpha + \beta\right)} - 5 \, c_{1} k_{1} e^{\left(2 \, \alpha + \beta\right)}\right)} k_{2}^{10} + 3 \, c_{0} k_{1}^{9} e^{\left(2 \, \alpha + \beta\right)} + {\left(19 \, k_{1}^{4} e^{\left(2 \, \alpha + \beta\right)} - 5 \, c_{1} k_{1}^{2} e^{\left(2 \, \alpha + \beta\right)} - 3 \, c_{0} e^{\left(2 \, \alpha + \beta\right)}\right)} k_{2}^{9} - 2 \, {\left(k_{1}^{5} e^{\left(2 \, \alpha + \beta\right)} - 8 \, c_{1} k_{1}^{3} e^{\left(2 \, \alpha + \beta\right)} + 5 \, c_{0} k_{1} e^{\left(2 \, \alpha + \beta\right)}\right)} k_{2}^{8} - {\left(7 \, k_{1}^{6} e^{\left(2 \, \alpha + \beta\right)} - 23 \, c_{1} k_{1}^{4} e^{\left(2 \, \alpha + \beta\right)} + c_{0} k_{1}^{2} e^{\left(2 \, \alpha + \beta\right)}\right)} k_{2}^{7} + {\left(7 \, k_{1}^{7} e^{\left(2 \, \alpha + \beta\right)} + 9 \, c_{1} k_{1}^{5} e^{\left(2 \, \alpha + \beta\right)} + 27 \, c_{0} k_{1}^{3} e^{\left(2 \, \alpha + \beta\right)}\right)} k_{2}^{6} + {\left(2 \, k_{1}^{8} e^{\left(2 \, \alpha + \beta\right)} - 9 \, c_{1} k_{1}^{6} e^{\left(2 \, \alpha + \beta\right)} + 21 \, c_{0} k_{1}^{4} e^{\left(2 \, \alpha + \beta\right)}\right)} k_{2}^{5} - {\left(19 \, k_{1}^{9} e^{\left(2 \, \alpha + \beta\right)} + 23 \, c_{1} k_{1}^{7} e^{\left(2 \, \alpha + \beta\right)} + 21 \, c_{0} k_{1}^{5} e^{\left(2 \, \alpha + \beta\right)}\right)} k_{2}^{4} - {\left(16 \, k_{1}^{10} e^{\left(2 \, \alpha + \beta\right)} + 16 \, c_{1} k_{1}^{8} e^{\left(2 \, \alpha + \beta\right)} + 27 \, c_{0} k_{1}^{6} e^{\left(2 \, \alpha + \beta\right)}\right)} k_{2}^{3} + {\left(5 \, k_{1}^{11} e^{\left(2 \, \alpha + \beta\right)} + 5 \, c_{1} k_{1}^{9} e^{\left(2 \, \alpha + \beta\right)} + c_{0} k_{1}^{7} e^{\left(2 \, \alpha + \beta\right)}\right)} k_{2}^{2} + 10 \, {\left(k_{1}^{12} e^{\left(2 \, \alpha + \beta\right)} + c_{1} k_{1}^{10} e^{\left(2 \, \alpha + \beta\right)} + c_{0} k_{1}^{8} e^{\left(2 \, \alpha + \beta\right)}\right)} k_{2}\right)} e^{\left(2 \, k_{1} x\right)} + {\left(3 \, k_{1}^{13} e^{\left(\alpha + \beta\right)} + 14 \, k_{1} k_{2}^{12} e^{\left(\alpha + \beta\right)} + 3 \, k_{2}^{13} e^{\left(\alpha + \beta\right)} + 3 \, c_{1} k_{1}^{11} e^{\left(\alpha + \beta\right)} + 14 \, c_{1} k_{1} k_{2}^{10} e^{\left(\alpha + \beta\right)} + 3 \, {\left(7 \, k_{1}^{2} e^{\left(\alpha + \beta\right)} + c_{1} e^{\left(\alpha + \beta\right)}\right)} k_{2}^{11} + 3 \, c_{0} k_{1}^{9} e^{\left(\alpha + \beta\right)} - 21 \, c_{0} k_{1}^{6} k_{2}^{3} e^{\left(\alpha + \beta\right)} - {\left(35 \, k_{1}^{4} e^{\left(\alpha + \beta\right)} - 21 \, c_{1} k_{1}^{2} e^{\left(\alpha + \beta\right)} - 3 \, c_{0} e^{\left(\alpha + \beta\right)}\right)} k_{2}^{9} - 14 \, {\left(3 \, k_{1}^{5} e^{\left(\alpha + \beta\right)} - c_{0} k_{1} e^{\left(\alpha + \beta\right)}\right)} k_{2}^{8} - {\left(25 \, k_{1}^{6} e^{\left(\alpha + \beta\right)} + 39 \, c_{1} k_{1}^{4} e^{\left(\alpha + \beta\right)} - 17 \, c_{0} k_{1}^{2} e^{\left(\alpha + \beta\right)}\right)} k_{2}^{7} - {\left(25 \, k_{1}^{7} e^{\left(\alpha + \beta\right)} + 63 \, c_{1} k_{1}^{5} e^{\left(\alpha + \beta\right)} + 21 \, c_{0} k_{1}^{3} e^{\left(\alpha + \beta\right)}\right)} k_{2}^{6} - 7 \, {\left(6 \, k_{1}^{8} e^{\left(\alpha + \beta\right)} + 9 \, c_{1} k_{1}^{6} e^{\left(\alpha + \beta\right)} + 11 \, c_{0} k_{1}^{4} e^{\left(\alpha + \beta\right)}\right)} k_{2}^{5} - {\left(35 \, k_{1}^{9} e^{\left(\alpha + \beta\right)} + 39 \, c_{1} k_{1}^{7} e^{\left(\alpha + \beta\right)} + 77 \, c_{0} k_{1}^{5} e^{\left(\alpha + \beta\right)}\right)} k_{2}^{4} + {\left(21 \, k_{1}^{11} e^{\left(\alpha + \beta\right)} + 21 \, c_{1} k_{1}^{9} e^{\left(\alpha + \beta\right)} + 17 \, c_{0} k_{1}^{7} e^{\left(\alpha + \beta\right)}\right)} k_{2}^{2} + 14 \, {\left(k_{1}^{12} e^{\left(\alpha + \beta\right)} + c_{1} k_{1}^{10} e^{\left(\alpha + \beta\right)} + c_{0} k_{1}^{8} e^{\left(\alpha + \beta\right)}\right)} k_{2}\right)} e^{\left(k_{1} x\right)}\right)} e^{\left(k_{2} x\right)} + {\left(6 \, k_{1} k_{2}^{12} e^{\left(2 \, \beta\right)} + k_{2}^{13} e^{\left(2 \, \beta\right)} + {\left(15 \, k_{1}^{2} e^{\left(2 \, \beta\right)} + c_{1} e^{\left(2 \, \beta\right)}\right)} k_{2}^{11} + 2 \, {\left(10 \, k_{1}^{3} e^{\left(2 \, \beta\right)} + 3 \, c_{1} k_{1} e^{\left(2 \, \beta\right)}\right)} k_{2}^{10} + c_{0} k_{1}^{6} k_{2}^{3} e^{\left(2 \, \beta\right)} + 6 \, c_{0} k_{1}^{5} k_{2}^{4} e^{\left(2 \, \beta\right)} + {\left(15 \, k_{1}^{4} e^{\left(2 \, \beta\right)} + 15 \, c_{1} k_{1}^{2} e^{\left(2 \, \beta\right)} + c_{0} e^{\left(2 \, \beta\right)}\right)} k_{2}^{9} + 2 \, {\left(3 \, k_{1}^{5} e^{\left(2 \, \beta\right)} + 10 \, c_{1} k_{1}^{3} e^{\left(2 \, \beta\right)} + 3 \, c_{0} k_{1} e^{\left(2 \, \beta\right)}\right)} k_{2}^{8} + {\left(k_{1}^{6} e^{\left(2 \, \beta\right)} + 15 \, c_{1} k_{1}^{4} e^{\left(2 \, \beta\right)} + 15 \, c_{0} k_{1}^{2} e^{\left(2 \, \beta\right)}\right)} k_{2}^{7} + 2 \, {\left(3 \, c_{1} k_{1}^{5} e^{\left(2 \, \beta\right)} + 10 \, c_{0} k_{1}^{3} e^{\left(2 \, \beta\right)}\right)} k_{2}^{6} + {\left(c_{1} k_{1}^{6} e^{\left(2 \, \beta\right)} + 15 \, c_{0} k_{1}^{4} e^{\left(2 \, \beta\right)}\right)} k_{2}^{5} - {\left(2 \, k_{1} k_{2}^{12} e^{\left(3 \, \alpha + 2 \, \beta\right)} - k_{2}^{13} e^{\left(3 \, \alpha + 2 \, \beta\right)} + {\left(k_{1}^{2} e^{\left(3 \, \alpha + 2 \, \beta\right)} - c_{1} e^{\left(3 \, \alpha + 2 \, \beta\right)}\right)} k_{2}^{11} - 2 \, {\left(2 \, k_{1}^{3} e^{\left(3 \, \alpha + 2 \, \beta\right)} - c_{1} k_{1} e^{\left(3 \, \alpha + 2 \, \beta\right)}\right)} k_{2}^{10} - c_{0} k_{1}^{6} k_{2}^{3} e^{\left(3 \, \alpha + 2 \, \beta\right)} + 2 \, c_{0} k_{1}^{5} k_{2}^{4} e^{\left(3 \, \alpha + 2 \, \beta\right)} + {\left(k_{1}^{4} e^{\left(3 \, \alpha + 2 \, \beta\right)} + c_{1} k_{1}^{2} e^{\left(3 \, \alpha + 2 \, \beta\right)} - c_{0} e^{\left(3 \, \alpha + 2 \, \beta\right)}\right)} k_{2}^{9} + 2 \, {\left(k_{1}^{5} e^{\left(3 \, \alpha + 2 \, \beta\right)} - 2 \, c_{1} k_{1}^{3} e^{\left(3 \, \alpha + 2 \, \beta\right)} + c_{0} k_{1} e^{\left(3 \, \alpha + 2 \, \beta\right)}\right)} k_{2}^{8} - {\left(k_{1}^{6} e^{\left(3 \, \alpha + 2 \, \beta\right)} - c_{1} k_{1}^{4} e^{\left(3 \, \alpha + 2 \, \beta\right)} - c_{0} k_{1}^{2} e^{\left(3 \, \alpha + 2 \, \beta\right)}\right)} k_{2}^{7} + 2 \, {\left(c_{1} k_{1}^{5} e^{\left(3 \, \alpha + 2 \, \beta\right)} - 2 \, c_{0} k_{1}^{3} e^{\left(3 \, \alpha + 2 \, \beta\right)}\right)} k_{2}^{6} - {\left(c_{1} k_{1}^{6} e^{\left(3 \, \alpha + 2 \, \beta\right)} - c_{0} k_{1}^{4} e^{\left(3 \, \alpha + 2 \, \beta\right)}\right)} k_{2}^{5}\right)} e^{\left(3 \, k_{1} x\right)} + {\left(3 \, k_{1}^{13} e^{\left(2 \, \alpha + 2 \, \beta\right)} + 2 \, k_{1} k_{2}^{12} e^{\left(2 \, \alpha + 2 \, \beta\right)} + 3 \, k_{2}^{13} e^{\left(2 \, \alpha + 2 \, \beta\right)} + 3 \, c_{1} k_{1}^{11} e^{\left(2 \, \alpha + 2 \, \beta\right)} - {\left(11 \, k_{1}^{2} e^{\left(2 \, \alpha + 2 \, \beta\right)} - 3 \, c_{1} e^{\left(2 \, \alpha + 2 \, \beta\right)}\right)} k_{2}^{11} - 2 \, {\left(4 \, k_{1}^{3} e^{\left(2 \, \alpha + 2 \, \beta\right)} - c_{1} k_{1} e^{\left(2 \, \alpha + 2 \, \beta\right)}\right)} k_{2}^{10} + 3 \, c_{0} k_{1}^{9} e^{\left(2 \, \alpha + 2 \, \beta\right)} + {\left(13 \, k_{1}^{4} e^{\left(2 \, \alpha + 2 \, \beta\right)} - 11 \, c_{1} k_{1}^{2} e^{\left(2 \, \alpha + 2 \, \beta\right)} + 3 \, c_{0} e^{\left(2 \, \alpha + 2 \, \beta\right)}\right)} k_{2}^{9} + 2 \, {\left(5 \, k_{1}^{5} e^{\left(2 \, \alpha + 2 \, \beta\right)} - 4 \, c_{1} k_{1}^{3} e^{\left(2 \, \alpha + 2 \, \beta\right)} + c_{0} k_{1} e^{\left(2 \, \alpha + 2 \, \beta\right)}\right)} k_{2}^{8} - 3 \, {\left(3 \, k_{1}^{6} e^{\left(2 \, \alpha + 2 \, \beta\right)} - 3 \, c_{1} k_{1}^{4} e^{\left(2 \, \alpha + 2 \, \beta\right)} + 5 \, c_{0} k_{1}^{2} e^{\left(2 \, \alpha + 2 \, \beta\right)}\right)} k_{2}^{7} - {\left(9 \, k_{1}^{7} e^{\left(2 \, \alpha + 2 \, \beta\right)} - 5 \, c_{1} k_{1}^{5} e^{\left(2 \, \alpha + 2 \, \beta\right)} + 13 \, c_{0} k_{1}^{3} e^{\left(2 \, \alpha + 2 \, \beta\right)}\right)} k_{2}^{6} + {\left(10 \, k_{1}^{8} e^{\left(2 \, \alpha + 2 \, \beta\right)} + 5 \, c_{1} k_{1}^{6} e^{\left(2 \, \alpha + 2 \, \beta\right)} + 23 \, c_{0} k_{1}^{4} e^{\left(2 \, \alpha + 2 \, \beta\right)}\right)} k_{2}^{5} + {\left(13 \, k_{1}^{9} e^{\left(2 \, \alpha + 2 \, \beta\right)} + 9 \, c_{1} k_{1}^{7} e^{\left(2 \, \alpha + 2 \, \beta\right)} + 23 \, c_{0} k_{1}^{5} e^{\left(2 \, \alpha + 2 \, \beta\right)}\right)} k_{2}^{4} - {\left(8 \, k_{1}^{10} e^{\left(2 \, \alpha + 2 \, \beta\right)} + 8 \, c_{1} k_{1}^{8} e^{\left(2 \, \alpha + 2 \, \beta\right)} + 13 \, c_{0} k_{1}^{6} e^{\left(2 \, \alpha + 2 \, \beta\right)}\right)} k_{2}^{3} - {\left(11 \, k_{1}^{11} e^{\left(2 \, \alpha + 2 \, \beta\right)} + 11 \, c_{1} k_{1}^{9} e^{\left(2 \, \alpha + 2 \, \beta\right)} + 15 \, c_{0} k_{1}^{7} e^{\left(2 \, \alpha + 2 \, \beta\right)}\right)} k_{2}^{2} + 2 \, {\left(k_{1}^{12} e^{\left(2 \, \alpha + 2 \, \beta\right)} + c_{1} k_{1}^{10} e^{\left(2 \, \alpha + 2 \, \beta\right)} + c_{0} k_{1}^{8} e^{\left(2 \, \alpha + 2 \, \beta\right)}\right)} k_{2}\right)} e^{\left(2 \, k_{1} x\right)} - {\left(3 \, k_{1}^{13} e^{\left(\alpha + 2 \, \beta\right)} - 10 \, k_{1} k_{2}^{12} e^{\left(\alpha + 2 \, \beta\right)} - 3 \, k_{2}^{13} e^{\left(\alpha + 2 \, \beta\right)} + 3 \, c_{1} k_{1}^{11} e^{\left(\alpha + 2 \, \beta\right)} - {\left(5 \, k_{1}^{2} e^{\left(\alpha + 2 \, \beta\right)} + 3 \, c_{1} e^{\left(\alpha + 2 \, \beta\right)}\right)} k_{2}^{11} + 2 \, {\left(8 \, k_{1}^{3} e^{\left(\alpha + 2 \, \beta\right)} - 5 \, c_{1} k_{1} e^{\left(\alpha + 2 \, \beta\right)}\right)} k_{2}^{10} + 3 \, c_{0} k_{1}^{9} e^{\left(\alpha + 2 \, \beta\right)} + {\left(19 \, k_{1}^{4} e^{\left(\alpha + 2 \, \beta\right)} - 5 \, c_{1} k_{1}^{2} e^{\left(\alpha + 2 \, \beta\right)} - 3 \, c_{0} e^{\left(\alpha + 2 \, \beta\right)}\right)} k_{2}^{9} - 2 \, {\left(k_{1}^{5} e^{\left(\alpha + 2 \, \beta\right)} - 8 \, c_{1} k_{1}^{3} e^{\left(\alpha + 2 \, \beta\right)} + 5 \, c_{0} k_{1} e^{\left(\alpha + 2 \, \beta\right)}\right)} k_{2}^{8} - {\left(7 \, k_{1}^{6} e^{\left(\alpha + 2 \, \beta\right)} - 23 \, c_{1} k_{1}^{4} e^{\left(\alpha + 2 \, \beta\right)} + c_{0} k_{1}^{2} e^{\left(\alpha + 2 \, \beta\right)}\right)} k_{2}^{7} + {\left(7 \, k_{1}^{7} e^{\left(\alpha + 2 \, \beta\right)} + 9 \, c_{1} k_{1}^{5} e^{\left(\alpha + 2 \, \beta\right)} + 27 \, c_{0} k_{1}^{3} e^{\left(\alpha + 2 \, \beta\right)}\right)} k_{2}^{6} + {\left(2 \, k_{1}^{8} e^{\left(\alpha + 2 \, \beta\right)} - 9 \, c_{1} k_{1}^{6} e^{\left(\alpha + 2 \, \beta\right)} + 21 \, c_{0} k_{1}^{4} e^{\left(\alpha + 2 \, \beta\right)}\right)} k_{2}^{5} - {\left(19 \, k_{1}^{9} e^{\left(\alpha + 2 \, \beta\right)} + 23 \, c_{1} k_{1}^{7} e^{\left(\alpha + 2 \, \beta\right)} + 21 \, c_{0} k_{1}^{5} e^{\left(\alpha + 2 \, \beta\right)}\right)} k_{2}^{4} - {\left(16 \, k_{1}^{10} e^{\left(\alpha + 2 \, \beta\right)} + 16 \, c_{1} k_{1}^{8} e^{\left(\alpha + 2 \, \beta\right)} + 27 \, c_{0} k_{1}^{6} e^{\left(\alpha + 2 \, \beta\right)}\right)} k_{2}^{3} + {\left(5 \, k_{1}^{11} e^{\left(\alpha + 2 \, \beta\right)} + 5 \, c_{1} k_{1}^{9} e^{\left(\alpha + 2 \, \beta\right)} + c_{0} k_{1}^{7} e^{\left(\alpha + 2 \, \beta\right)}\right)} k_{2}^{2} + 10 \, {\left(k_{1}^{12} e^{\left(\alpha + 2 \, \beta\right)} + c_{1} k_{1}^{10} e^{\left(\alpha + 2 \, \beta\right)} + c_{0} k_{1}^{8} e^{\left(\alpha + 2 \, \beta\right)}\right)} k_{2}\right)} e^{\left(k_{1} x\right)}\right)} e^{\left(2 \, k_{2} x\right)}\right)}}{k_{1}^{6} + 6 \, k_{1}^{5} k_{2} + 15 \, k_{1}^{4} k_{2}^{2} + 20 \, k_{1}^{3} k_{2}^{3} + 15 \, k_{1}^{2} k_{2}^{4} + 6 \, k_{1} k_{2}^{5} + k_{2}^{6} + 3 \, {\left(k_{1}^{6} e^{\alpha} + 6 \, k_{1}^{5} k_{2} e^{\alpha} + 15 \, k_{1}^{4} k_{2}^{2} e^{\alpha} + 20 \, k_{1}^{3} k_{2}^{3} e^{\alpha} + 15 \, k_{1}^{2} k_{2}^{4} e^{\alpha} + 6 \, k_{1} k_{2}^{5} e^{\alpha} + k_{2}^{6} e^{\alpha}\right)} e^{\left(k_{1} x\right)} + {\left(k_{1}^{6} e^{\left(3 \, \alpha\right)} + 6 \, k_{1}^{5} k_{2} e^{\left(3 \, \alpha\right)} + 15 \, k_{1}^{4} k_{2}^{2} e^{\left(3 \, \alpha\right)} + 20 \, k_{1}^{3} k_{2}^{3} e^{\left(3 \, \alpha\right)} + 15 \, k_{1}^{2} k_{2}^{4} e^{\left(3 \, \alpha\right)} + 6 \, k_{1} k_{2}^{5} e^{\left(3 \, \alpha\right)} + k_{2}^{6} e^{\left(3 \, \alpha\right)}\right)} e^{\left(3 \, k_{1} x\right)} + 3 \, {\left(k_{1}^{6} e^{\left(2 \, \alpha\right)} + 6 \, k_{1}^{5} k_{2} e^{\left(2 \, \alpha\right)} + 15 \, k_{1}^{4} k_{2}^{2} e^{\left(2 \, \alpha\right)} + 20 \, k_{1}^{3} k_{2}^{3} e^{\left(2 \, \alpha\right)} + 15 \, k_{1}^{2} k_{2}^{4} e^{\left(2 \, \alpha\right)} + 6 \, k_{1} k_{2}^{5} e^{\left(2 \, \alpha\right)} + k_{2}^{6} e^{\left(2 \, \alpha\right)}\right)} e^{\left(2 \, k_{1} x\right)} + 3 \, {\left(k_{1}^{6} e^{\beta} + 6 \, k_{1}^{5} k_{2} e^{\beta} + 15 \, k_{1}^{4} k_{2}^{2} e^{\beta} + 20 \, k_{1}^{3} k_{2}^{3} e^{\beta} + 15 \, k_{1}^{2} k_{2}^{4} e^{\beta} + 6 \, k_{1} k_{2}^{5} e^{\beta} + k_{2}^{6} e^{\beta} + {\left(k_{1}^{6} e^{\left(3 \, \alpha + \beta\right)} + 2 \, k_{1}^{5} k_{2} e^{\left(3 \, \alpha + \beta\right)} - k_{1}^{4} k_{2}^{2} e^{\left(3 \, \alpha + \beta\right)} - 4 \, k_{1}^{3} k_{2}^{3} e^{\left(3 \, \alpha + \beta\right)} - k_{1}^{2} k_{2}^{4} e^{\left(3 \, \alpha + \beta\right)} + 2 \, k_{1} k_{2}^{5} e^{\left(3 \, \alpha + \beta\right)} + k_{2}^{6} e^{\left(3 \, \alpha + \beta\right)}\right)} e^{\left(3 \, k_{1} x\right)} + {\left(3 \, k_{1}^{6} e^{\left(2 \, \alpha + \beta\right)} + 10 \, k_{1}^{5} k_{2} e^{\left(2 \, \alpha + \beta\right)} + 13 \, k_{1}^{4} k_{2}^{2} e^{\left(2 \, \alpha + \beta\right)} + 12 \, k_{1}^{3} k_{2}^{3} e^{\left(2 \, \alpha + \beta\right)} + 13 \, k_{1}^{2} k_{2}^{4} e^{\left(2 \, \alpha + \beta\right)} + 10 \, k_{1} k_{2}^{5} e^{\left(2 \, \alpha + \beta\right)} + 3 \, k_{2}^{6} e^{\left(2 \, \alpha + \beta\right)}\right)} e^{\left(2 \, k_{1} x\right)} + {\left(3 \, k_{1}^{6} e^{\left(\alpha + \beta\right)} + 14 \, k_{1}^{5} k_{2} e^{\left(\alpha + \beta\right)} + 29 \, k_{1}^{4} k_{2}^{2} e^{\left(\alpha + \beta\right)} + 36 \, k_{1}^{3} k_{2}^{3} e^{\left(\alpha + \beta\right)} + 29 \, k_{1}^{2} k_{2}^{4} e^{\left(\alpha + \beta\right)} + 14 \, k_{1} k_{2}^{5} e^{\left(\alpha + \beta\right)} + 3 \, k_{2}^{6} e^{\left(\alpha + \beta\right)}\right)} e^{\left(k_{1} x\right)}\right)} e^{\left(k_{2} x\right)} + {\left(k_{1}^{6} e^{\left(3 \, \beta\right)} + 6 \, k_{1}^{5} k_{2} e^{\left(3 \, \beta\right)} + 15 \, k_{1}^{4} k_{2}^{2} e^{\left(3 \, \beta\right)} + 20 \, k_{1}^{3} k_{2}^{3} e^{\left(3 \, \beta\right)} + 15 \, k_{1}^{2} k_{2}^{4} e^{\left(3 \, \beta\right)} + 6 \, k_{1} k_{2}^{5} e^{\left(3 \, \beta\right)} + k_{2}^{6} e^{\left(3 \, \beta\right)} + {\left(k_{1}^{6} e^{\left(3 \, \alpha + 3 \, \beta\right)} - 6 \, k_{1}^{5} k_{2} e^{\left(3 \, \alpha + 3 \, \beta\right)} + 15 \, k_{1}^{4} k_{2}^{2} e^{\left(3 \, \alpha + 3 \, \beta\right)} - 20 \, k_{1}^{3} k_{2}^{3} e^{\left(3 \, \alpha + 3 \, \beta\right)} + 15 \, k_{1}^{2} k_{2}^{4} e^{\left(3 \, \alpha + 3 \, \beta\right)} - 6 \, k_{1} k_{2}^{5} e^{\left(3 \, \alpha + 3 \, \beta\right)} + k_{2}^{6} e^{\left(3 \, \alpha + 3 \, \beta\right)}\right)} e^{\left(3 \, k_{1} x\right)} + 3 \, {\left(k_{1}^{6} e^{\left(2 \, \alpha + 3 \, \beta\right)} - 2 \, k_{1}^{5} k_{2} e^{\left(2 \, \alpha + 3 \, \beta\right)} - k_{1}^{4} k_{2}^{2} e^{\left(2 \, \alpha + 3 \, \beta\right)} + 4 \, k_{1}^{3} k_{2}^{3} e^{\left(2 \, \alpha + 3 \, \beta\right)} - k_{1}^{2} k_{2}^{4} e^{\left(2 \, \alpha + 3 \, \beta\right)} - 2 \, k_{1} k_{2}^{5} e^{\left(2 \, \alpha + 3 \, \beta\right)} + k_{2}^{6} e^{\left(2 \, \alpha + 3 \, \beta\right)}\right)} e^{\left(2 \, k_{1} x\right)} + 3 \, {\left(k_{1}^{6} e^{\left(\alpha + 3 \, \beta\right)} + 2 \, k_{1}^{5} k_{2} e^{\left(\alpha + 3 \, \beta\right)} - k_{1}^{4} k_{2}^{2} e^{\left(\alpha + 3 \, \beta\right)} - 4 \, k_{1}^{3} k_{2}^{3} e^{\left(\alpha + 3 \, \beta\right)} - k_{1}^{2} k_{2}^{4} e^{\left(\alpha + 3 \, \beta\right)} + 2 \, k_{1} k_{2}^{5} e^{\left(\alpha + 3 \, \beta\right)} + k_{2}^{6} e^{\left(\alpha + 3 \, \beta\right)}\right)} e^{\left(k_{1} x\right)}\right)} e^{\left(3 \, k_{2} x\right)} + 3 \, {\left(k_{1}^{6} e^{\left(2 \, \beta\right)} + 6 \, k_{1}^{5} k_{2} e^{\left(2 \, \beta\right)} + 15 \, k_{1}^{4} k_{2}^{2} e^{\left(2 \, \beta\right)} + 20 \, k_{1}^{3} k_{2}^{3} e^{\left(2 \, \beta\right)} + 15 \, k_{1}^{2} k_{2}^{4} e^{\left(2 \, \beta\right)} + 6 \, k_{1} k_{2}^{5} e^{\left(2 \, \beta\right)} + k_{2}^{6} e^{\left(2 \, \beta\right)} + {\left(k_{1}^{6} e^{\left(3 \, \alpha + 2 \, \beta\right)} - 2 \, k_{1}^{5} k_{2} e^{\left(3 \, \alpha + 2 \, \beta\right)} - k_{1}^{4} k_{2}^{2} e^{\left(3 \, \alpha + 2 \, \beta\right)} + 4 \, k_{1}^{3} k_{2}^{3} e^{\left(3 \, \alpha + 2 \, \beta\right)} - k_{1}^{2} k_{2}^{4} e^{\left(3 \, \alpha + 2 \, \beta\right)} - 2 \, k_{1} k_{2}^{5} e^{\left(3 \, \alpha + 2 \, \beta\right)} + k_{2}^{6} e^{\left(3 \, \alpha + 2 \, \beta\right)}\right)} e^{\left(3 \, k_{1} x\right)} + {\left(3 \, k_{1}^{6} e^{\left(2 \, \alpha + 2 \, \beta\right)} + 2 \, k_{1}^{5} k_{2} e^{\left(2 \, \alpha + 2 \, \beta\right)} - 3 \, k_{1}^{4} k_{2}^{2} e^{\left(2 \, \alpha + 2 \, \beta\right)} - 4 \, k_{1}^{3} k_{2}^{3} e^{\left(2 \, \alpha + 2 \, \beta\right)} - 3 \, k_{1}^{2} k_{2}^{4} e^{\left(2 \, \alpha + 2 \, \beta\right)} + 2 \, k_{1} k_{2}^{5} e^{\left(2 \, \alpha + 2 \, \beta\right)} + 3 \, k_{2}^{6} e^{\left(2 \, \alpha + 2 \, \beta\right)}\right)} e^{\left(2 \, k_{1} x\right)} + {\left(3 \, k_{1}^{6} e^{\left(\alpha + 2 \, \beta\right)} + 10 \, k_{1}^{5} k_{2} e^{\left(\alpha + 2 \, \beta\right)} + 13 \, k_{1}^{4} k_{2}^{2} e^{\left(\alpha + 2 \, \beta\right)} + 12 \, k_{1}^{3} k_{2}^{3} e^{\left(\alpha + 2 \, \beta\right)} + 13 \, k_{1}^{2} k_{2}^{4} e^{\left(\alpha + 2 \, \beta\right)} + 10 \, k_{1} k_{2}^{5} e^{\left(\alpha + 2 \, \beta\right)} + 3 \, k_{2}^{6} e^{\left(\alpha + 2 \, \beta\right)}\right)} e^{\left(k_{1} x\right)}\right)} e^{\left(2 \, k_{2} x\right)}}

d = solve([bigeqn==0], c_0, c_1, solution_dict=True)[0][0]

show(d[c_0].simplify_full())

\newcommand{\Bold}[1]{\mathbf{#1}}-\frac{{\left({\left(k_{1}^{11} e^{\left(\alpha + 3 \, \beta\right)} + c_{1} k_{1}^{9} e^{\left(\alpha + 3 \, \beta\right)} + {\left(k_{1}^{7} e^{\left(\alpha + 3 \, \beta\right)} + c_{1} k_{1}^{5} e^{\left(\alpha + 3 \, \beta\right)}\right)} k_{2}^{4} - 2 \, {\left(k_{1}^{9} e^{\left(\alpha + 3 \, \beta\right)} + c_{1} k_{1}^{7} e^{\left(\alpha + 3 \, \beta\right)}\right)} k_{2}^{2}\right)} e^{\left(k_{1} x\right)} - {\left(k_{1}^{11} e^{\left(2 \, \alpha + 3 \, \beta\right)} + c_{1} k_{1}^{9} e^{\left(2 \, \alpha + 3 \, \beta\right)} + {\left(k_{1}^{7} e^{\left(2 \, \alpha + 3 \, \beta\right)} + c_{1} k_{1}^{5} e^{\left(2 \, \alpha + 3 \, \beta\right)}\right)} k_{2}^{4} - 4 \, {\left(k_{1}^{8} e^{\left(2 \, \alpha + 3 \, \beta\right)} + c_{1} k_{1}^{6} e^{\left(2 \, \alpha + 3 \, \beta\right)}\right)} k_{2}^{3} + 6 \, {\left(k_{1}^{9} e^{\left(2 \, \alpha + 3 \, \beta\right)} + c_{1} k_{1}^{7} e^{\left(2 \, \alpha + 3 \, \beta\right)}\right)} k_{2}^{2} - 4 \, {\left(k_{1}^{10} e^{\left(2 \, \alpha + 3 \, \beta\right)} + c_{1} k_{1}^{8} e^{\left(2 \, \alpha + 3 \, \beta\right)}\right)} k_{2}\right)} e^{\left(2 \, k_{1} x\right)}\right)} e^{\left(3 \, k_{2} x\right)} + {\left(k_{1}^{11} e^{\alpha} + c_{1} k_{1}^{9} e^{\alpha} + {\left(k_{1}^{7} e^{\alpha} + c_{1} k_{1}^{5} e^{\alpha}\right)} k_{2}^{4} + 4 \, {\left(k_{1}^{8} e^{\alpha} + c_{1} k_{1}^{6} e^{\alpha}\right)} k_{2}^{3} + 6 \, {\left(k_{1}^{9} e^{\alpha} + c_{1} k_{1}^{7} e^{\alpha}\right)} k_{2}^{2} + 4 \, {\left(k_{1}^{10} e^{\alpha} + c_{1} k_{1}^{8} e^{\alpha}\right)} k_{2}\right)} e^{\left(k_{1} x\right)} - {\left(k_{1}^{11} e^{\left(2 \, \alpha\right)} + c_{1} k_{1}^{9} e^{\left(2 \, \alpha\right)} + {\left(k_{1}^{7} e^{\left(2 \, \alpha\right)} + c_{1} k_{1}^{5} e^{\left(2 \, \alpha\right)}\right)} k_{2}^{4} + 4 \, {\left(k_{1}^{8} e^{\left(2 \, \alpha\right)} + c_{1} k_{1}^{6} e^{\left(2 \, \alpha\right)}\right)} k_{2}^{3} + 6 \, {\left(k_{1}^{9} e^{\left(2 \, \alpha\right)} + c_{1} k_{1}^{7} e^{\left(2 \, \alpha\right)}\right)} k_{2}^{2} + 4 \, {\left(k_{1}^{10} e^{\left(2 \, \alpha\right)} + c_{1} k_{1}^{8} e^{\left(2 \, \alpha\right)}\right)} k_{2}\right)} e^{\left(2 \, k_{1} x\right)} + {\left(4 \, k_{1} k_{2}^{10} e^{\beta} + k_{2}^{11} e^{\beta} + c_{1} k_{1}^{4} k_{2}^{5} e^{\beta} + 4 \, c_{1} k_{1}^{3} k_{2}^{6} e^{\beta} + {\left(6 \, k_{1}^{2} e^{\beta} + c_{1} e^{\beta}\right)} k_{2}^{9} + 4 \, {\left(k_{1}^{3} e^{\beta} + c_{1} k_{1} e^{\beta}\right)} k_{2}^{8} + {\left(k_{1}^{4} e^{\beta} + 6 \, c_{1} k_{1}^{2} e^{\beta}\right)} k_{2}^{7} + {\left(k_{2}^{11} e^{\left(3 \, \alpha + \beta\right)} + c_{1} k_{1}^{4} k_{2}^{5} e^{\left(3 \, \alpha + \beta\right)} - {\left(2 \, k_{1}^{2} e^{\left(3 \, \alpha + \beta\right)} - c_{1} e^{\left(3 \, \alpha + \beta\right)}\right)} k_{2}^{9} + {\left(k_{1}^{4} e^{\left(3 \, \alpha + \beta\right)} - 2 \, c_{1} k_{1}^{2} e^{\left(3 \, \alpha + \beta\right)}\right)} k_{2}^{7}\right)} e^{\left(3 \, k_{1} x\right)} - {\left(3 \, k_{1}^{11} e^{\left(2 \, \alpha + \beta\right)} - 4 \, k_{1} k_{2}^{10} e^{\left(2 \, \alpha + \beta\right)} - 3 \, k_{2}^{11} e^{\left(2 \, \alpha + \beta\right)} + 3 \, c_{1} k_{1}^{9} e^{\left(2 \, \alpha + \beta\right)} + 3 \, {\left(2 \, k_{1}^{2} e^{\left(2 \, \alpha + \beta\right)} - c_{1} e^{\left(2 \, \alpha + \beta\right)}\right)} k_{2}^{9} + 4 \, {\left(2 \, k_{1}^{3} e^{\left(2 \, \alpha + \beta\right)} - c_{1} k_{1} e^{\left(2 \, \alpha + \beta\right)}\right)} k_{2}^{8} - 3 \, {\left(k_{1}^{4} e^{\left(2 \, \alpha + \beta\right)} - 2 \, c_{1} k_{1}^{2} e^{\left(2 \, \alpha + \beta\right)}\right)} k_{2}^{7} - 4 \, {\left(k_{1}^{5} e^{\left(2 \, \alpha + \beta\right)} - 2 \, c_{1} k_{1}^{3} e^{\left(2 \, \alpha + \beta\right)}\right)} k_{2}^{6} + {\left(4 \, k_{1}^{6} e^{\left(2 \, \alpha + \beta\right)} + c_{1} k_{1}^{4} e^{\left(2 \, \alpha + \beta\right)}\right)} k_{2}^{5} + {\left(3 \, k_{1}^{7} e^{\left(2 \, \alpha + \beta\right)} - c_{1} k_{1}^{5} e^{\left(2 \, \alpha + \beta\right)}\right)} k_{2}^{4} - 8 \, {\left(k_{1}^{8} e^{\left(2 \, \alpha + \beta\right)} + c_{1} k_{1}^{6} e^{\left(2 \, \alpha + \beta\right)}\right)} k_{2}^{3} - 6 \, {\left(k_{1}^{9} e^{\left(2 \, \alpha + \beta\right)} + c_{1} k_{1}^{7} e^{\left(2 \, \alpha + \beta\right)}\right)} k_{2}^{2} + 4 \, {\left(k_{1}^{10} e^{\left(2 \, \alpha + \beta\right)} + c_{1} k_{1}^{8} e^{\left(2 \, \alpha + \beta\right)}\right)} k_{2}\right)} e^{\left(2 \, k_{1} x\right)} + {\left(3 \, k_{1}^{11} e^{\left(\alpha + \beta\right)} + 8 \, k_{1} k_{2}^{10} e^{\left(\alpha + \beta\right)} + 3 \, k_{2}^{11} e^{\left(\alpha + \beta\right)} + 3 \, c_{1} k_{1}^{9} e^{\left(\alpha + \beta\right)} + {\left(2 \, k_{1}^{2} e^{\left(\alpha + \beta\right)} + 3 \, c_{1} e^{\left(\alpha + \beta\right)}\right)} k_{2}^{9} - 4 \, {\left(3 \, k_{1}^{3} e^{\left(\alpha + \beta\right)} - 2 \, c_{1} k_{1} e^{\left(\alpha + \beta\right)}\right)} k_{2}^{8} - {\left(13 \, k_{1}^{4} e^{\left(\alpha + \beta\right)} - 2 \, c_{1} k_{1}^{2} e^{\left(\alpha + \beta\right)}\right)} k_{2}^{7} - 4 \, {\left(k_{1}^{5} e^{\left(\alpha + \beta\right)} + 3 \, c_{1} k_{1}^{3} e^{\left(\alpha + \beta\right)}\right)} k_{2}^{6} - {\left(4 \, k_{1}^{6} e^{\left(\alpha + \beta\right)} + 17 \, c_{1} k_{1}^{4} e^{\left(\alpha + \beta\right)}\right)} k_{2}^{5} - {\left(13 \, k_{1}^{7} e^{\left(\alpha + \beta\right)} + 17 \, c_{1} k_{1}^{5} e^{\left(\alpha + \beta\right)}\right)} k_{2}^{4} - 12 \, {\left(k_{1}^{8} e^{\left(\alpha + \beta\right)} + c_{1} k_{1}^{6} e^{\left(\alpha + \beta\right)}\right)} k_{2}^{3} + 2 \, {\left(k_{1}^{9} e^{\left(\alpha + \beta\right)} + c_{1} k_{1}^{7} e^{\left(\alpha + \beta\right)}\right)} k_{2}^{2} + 8 \, {\left(k_{1}^{10} e^{\left(\alpha + \beta\right)} + c_{1} k_{1}^{8} e^{\left(\alpha + \beta\right)}\right)} k_{2}\right)} e^{\left(k_{1} x\right)}\right)} e^{\left(k_{2} x\right)} - {\left(4 \, k_{1} k_{2}^{10} e^{\left(2 \, \beta\right)} + k_{2}^{11} e^{\left(2 \, \beta\right)} + c_{1} k_{1}^{4} k_{2}^{5} e^{\left(2 \, \beta\right)} + 4 \, c_{1} k_{1}^{3} k_{2}^{6} e^{\left(2 \, \beta\right)} + {\left(6 \, k_{1}^{2} e^{\left(2 \, \beta\right)} + c_{1} e^{\left(2 \, \beta\right)}\right)} k_{2}^{9} + 4 \, {\left(k_{1}^{3} e^{\left(2 \, \beta\right)} + c_{1} k_{1} e^{\left(2 \, \beta\right)}\right)} k_{2}^{8} + {\left(k_{1}^{4} e^{\left(2 \, \beta\right)} + 6 \, c_{1} k_{1}^{2} e^{\left(2 \, \beta\right)}\right)} k_{2}^{7} - {\left(4 \, k_{1} k_{2}^{10} e^{\left(3 \, \alpha + 2 \, \beta\right)} - k_{2}^{11} e^{\left(3 \, \alpha + 2 \, \beta\right)} - c_{1} k_{1}^{4} k_{2}^{5} e^{\left(3 \, \alpha + 2 \, \beta\right)} + 4 \, c_{1} k_{1}^{3} k_{2}^{6} e^{\left(3 \, \alpha + 2 \, \beta\right)} - {\left(6 \, k_{1}^{2} e^{\left(3 \, \alpha + 2 \, \beta\right)} + c_{1} e^{\left(3 \, \alpha + 2 \, \beta\right)}\right)} k_{2}^{9} + 4 \, {\left(k_{1}^{3} e^{\left(3 \, \alpha + 2 \, \beta\right)} + c_{1} k_{1} e^{\left(3 \, \alpha + 2 \, \beta\right)}\right)} k_{2}^{8} - {\left(k_{1}^{4} e^{\left(3 \, \alpha + 2 \, \beta\right)} + 6 \, c_{1} k_{1}^{2} e^{\left(3 \, \alpha + 2 \, \beta\right)}\right)} k_{2}^{7}\right)} e^{\left(3 \, k_{1} x\right)} + {\left(3 \, k_{1}^{11} e^{\left(2 \, \alpha + 2 \, \beta\right)} - 4 \, k_{1} k_{2}^{10} e^{\left(2 \, \alpha + 2 \, \beta\right)} + 3 \, k_{2}^{11} e^{\left(2 \, \alpha + 2 \, \beta\right)} + 3 \, c_{1} k_{1}^{9} e^{\left(2 \, \alpha + 2 \, \beta\right)} - 3 \, {\left(2 \, k_{1}^{2} e^{\left(2 \, \alpha + 2 \, \beta\right)} - c_{1} e^{\left(2 \, \alpha + 2 \, \beta\right)}\right)} k_{2}^{9} + 4 \, {\left(2 \, k_{1}^{3} e^{\left(2 \, \alpha + 2 \, \beta\right)} - c_{1} k_{1} e^{\left(2 \, \alpha + 2 \, \beta\right)}\right)} k_{2}^{8} + 3 \, {\left(k_{1}^{4} e^{\left(2 \, \alpha + 2 \, \beta\right)} - 2 \, c_{1} k_{1}^{2} e^{\left(2 \, \alpha + 2 \, \beta\right)}\right)} k_{2}^{7} - 4 \, {\left(k_{1}^{5} e^{\left(2 \, \alpha + 2 \, \beta\right)} - 2 \, c_{1} k_{1}^{3} e^{\left(2 \, \alpha + 2 \, \beta\right)}\right)} k_{2}^{6} - {\left(4 \, k_{1}^{6} e^{\left(2 \, \alpha + 2 \, \beta\right)} + c_{1} k_{1}^{4} e^{\left(2 \, \alpha + 2 \, \beta\right)}\right)} k_{2}^{5} + {\left(3 \, k_{1}^{7} e^{\left(2 \, \alpha + 2 \, \beta\right)} - c_{1} k_{1}^{5} e^{\left(2 \, \alpha + 2 \, \beta\right)}\right)} k_{2}^{4} + 8 \, {\left(k_{1}^{8} e^{\left(2 \, \alpha + 2 \, \beta\right)} + c_{1} k_{1}^{6} e^{\left(2 \, \alpha + 2 \, \beta\right)}\right)} k_{2}^{3} - 6 \, {\left(k_{1}^{9} e^{\left(2 \, \alpha + 2 \, \beta\right)} + c_{1} k_{1}^{7} e^{\left(2 \, \alpha + 2 \, \beta\right)}\right)} k_{2}^{2} - 4 \, {\left(k_{1}^{10} e^{\left(2 \, \alpha + 2 \, \beta\right)} + c_{1} k_{1}^{8} e^{\left(2 \, \alpha + 2 \, \beta\right)}\right)} k_{2}\right)} e^{\left(2 \, k_{1} x\right)} - {\left(3 \, k_{1}^{11} e^{\left(\alpha + 2 \, \beta\right)} - 4 \, k_{1} k_{2}^{10} e^{\left(\alpha + 2 \, \beta\right)} - 3 \, k_{2}^{11} e^{\left(\alpha + 2 \, \beta\right)} + 3 \, c_{1} k_{1}^{9} e^{\left(\alpha + 2 \, \beta\right)} + 3 \, {\left(2 \, k_{1}^{2} e^{\left(\alpha + 2 \, \beta\right)} - c_{1} e^{\left(\alpha + 2 \, \beta\right)}\right)} k_{2}^{9} + 4 \, {\left(2 \, k_{1}^{3} e^{\left(\alpha + 2 \, \beta\right)} - c_{1} k_{1} e^{\left(\alpha + 2 \, \beta\right)}\right)} k_{2}^{8} - 3 \, {\left(k_{1}^{4} e^{\left(\alpha + 2 \, \beta\right)} - 2 \, c_{1} k_{1}^{2} e^{\left(\alpha + 2 \, \beta\right)}\right)} k_{2}^{7} - 4 \, {\left(k_{1}^{5} e^{\left(\alpha + 2 \, \beta\right)} - 2 \, c_{1} k_{1}^{3} e^{\left(\alpha + 2 \, \beta\right)}\right)} k_{2}^{6} + {\left(4 \, k_{1}^{6} e^{\left(\alpha + 2 \, \beta\right)} + c_{1} k_{1}^{4} e^{\left(\alpha + 2 \, \beta\right)}\right)} k_{2}^{5} + {\left(3 \, k_{1}^{7} e^{\left(\alpha + 2 \, \beta\right)} - c_{1} k_{1}^{5} e^{\left(\alpha + 2 \, \beta\right)}\right)} k_{2}^{4} - 8 \, {\left(k_{1}^{8} e^{\left(\alpha + 2 \, \beta\right)} + c_{1} k_{1}^{6} e^{\left(\alpha + 2 \, \beta\right)}\right)} k_{2}^{3} - 6 \, {\left(k_{1}^{9} e^{\left(\alpha + 2 \, \beta\right)} + c_{1} k_{1}^{7} e^{\left(\alpha + 2 \, \beta\right)}\right)} k_{2}^{2} + 4 \, {\left(k_{1}^{10} e^{\left(\alpha + 2 \, \beta\right)} + c_{1} k_{1}^{8} e^{\left(\alpha + 2 \, \beta\right)}\right)} k_{2}\right)} e^{\left(k_{1} x\right)}\right)} e^{\left(2 \, k_{2} x\right)}}{{\left({\left(k_{1}^{7} e^{\left(\alpha + 3 \, \beta\right)} - 2 \, k_{1}^{5} k_{2}^{2} e^{\left(\alpha + 3 \, \beta\right)} + k_{1}^{3} k_{2}^{4} e^{\left(\alpha + 3 \, \beta\right)}\right)} e^{\left(k_{1} x\right)} - {\left(k_{1}^{7} e^{\left(2 \, \alpha + 3 \, \beta\right)} - 4 \, k_{1}^{6} k_{2} e^{\left(2 \, \alpha + 3 \, \beta\right)} + 6 \, k_{1}^{5} k_{2}^{2} e^{\left(2 \, \alpha + 3 \, \beta\right)} - 4 \, k_{1}^{4} k_{2}^{3} e^{\left(2 \, \alpha + 3 \, \beta\right)} + k_{1}^{3} k_{2}^{4} e^{\left(2 \, \alpha + 3 \, \beta\right)}\right)} e^{\left(2 \, k_{1} x\right)}\right)} e^{\left(3 \, k_{2} x\right)} + {\left(k_{1}^{7} e^{\alpha} + 4 \, k_{1}^{6} k_{2} e^{\alpha} + 6 \, k_{1}^{5} k_{2}^{2} e^{\alpha} + 4 \, k_{1}^{4} k_{2}^{3} e^{\alpha} + k_{1}^{3} k_{2}^{4} e^{\alpha}\right)} e^{\left(k_{1} x\right)} - {\left(k_{1}^{7} e^{\left(2 \, \alpha\right)} + 4 \, k_{1}^{6} k_{2} e^{\left(2 \, \alpha\right)} + 6 \, k_{1}^{5} k_{2}^{2} e^{\left(2 \, \alpha\right)} + 4 \, k_{1}^{4} k_{2}^{3} e^{\left(2 \, \alpha\right)} + k_{1}^{3} k_{2}^{4} e^{\left(2 \, \alpha\right)}\right)} e^{\left(2 \, k_{1} x\right)} + {\left(k_{1}^{4} k_{2}^{3} e^{\beta} + 4 \, k_{1}^{3} k_{2}^{4} e^{\beta} + 6 \, k_{1}^{2} k_{2}^{5} e^{\beta} + 4 \, k_{1} k_{2}^{6} e^{\beta} + k_{2}^{7} e^{\beta} + {\left(k_{1}^{4} k_{2}^{3} e^{\left(3 \, \alpha + \beta\right)} - 2 \, k_{1}^{2} k_{2}^{5} e^{\left(3 \, \alpha + \beta\right)} + k_{2}^{7} e^{\left(3 \, \alpha + \beta\right)}\right)} e^{\left(3 \, k_{1} x\right)} - {\left(3 \, k_{1}^{7} e^{\left(2 \, \alpha + \beta\right)} + 4 \, k_{1}^{6} k_{2} e^{\left(2 \, \alpha + \beta\right)} - 10 \, k_{1}^{5} k_{2}^{2} e^{\left(2 \, \alpha + \beta\right)} - 11 \, k_{1}^{4} k_{2}^{3} e^{\left(2 \, \alpha + \beta\right)} + 11 \, k_{1}^{3} k_{2}^{4} e^{\left(2 \, \alpha + \beta\right)} + 10 \, k_{1}^{2} k_{2}^{5} e^{\left(2 \, \alpha + \beta\right)} - 4 \, k_{1} k_{2}^{6} e^{\left(2 \, \alpha + \beta\right)} - 3 \, k_{2}^{7} e^{\left(2 \, \alpha + \beta\right)}\right)} e^{\left(2 \, k_{1} x\right)} + {\left(3 \, k_{1}^{7} e^{\left(\alpha + \beta\right)} + 8 \, k_{1}^{6} k_{2} e^{\left(\alpha + \beta\right)} - 2 \, k_{1}^{5} k_{2}^{2} e^{\left(\alpha + \beta\right)} - 25 \, k_{1}^{4} k_{2}^{3} e^{\left(\alpha + \beta\right)} - 25 \, k_{1}^{3} k_{2}^{4} e^{\left(\alpha + \beta\right)} - 2 \, k_{1}^{2} k_{2}^{5} e^{\left(\alpha + \beta\right)} + 8 \, k_{1} k_{2}^{6} e^{\left(\alpha + \beta\right)} + 3 \, k_{2}^{7} e^{\left(\alpha + \beta\right)}\right)} e^{\left(k_{1} x\right)}\right)} e^{\left(k_{2} x\right)} - {\left(k_{1}^{4} k_{2}^{3} e^{\left(2 \, \beta\right)} + 4 \, k_{1}^{3} k_{2}^{4} e^{\left(2 \, \beta\right)} + 6 \, k_{1}^{2} k_{2}^{5} e^{\left(2 \, \beta\right)} + 4 \, k_{1} k_{2}^{6} e^{\left(2 \, \beta\right)} + k_{2}^{7} e^{\left(2 \, \beta\right)} + {\left(k_{1}^{4} k_{2}^{3} e^{\left(3 \, \alpha + 2 \, \beta\right)} - 4 \, k_{1}^{3} k_{2}^{4} e^{\left(3 \, \alpha + 2 \, \beta\right)} + 6 \, k_{1}^{2} k_{2}^{5} e^{\left(3 \, \alpha + 2 \, \beta\right)} - 4 \, k_{1} k_{2}^{6} e^{\left(3 \, \alpha + 2 \, \beta\right)} + k_{2}^{7} e^{\left(3 \, \alpha + 2 \, \beta\right)}\right)} e^{\left(3 \, k_{1} x\right)} + {\left(3 \, k_{1}^{7} e^{\left(2 \, \alpha + 2 \, \beta\right)} - 4 \, k_{1}^{6} k_{2} e^{\left(2 \, \alpha + 2 \, \beta\right)} - 10 \, k_{1}^{5} k_{2}^{2} e^{\left(2 \, \alpha + 2 \, \beta\right)} + 11 \, k_{1}^{4} k_{2}^{3} e^{\left(2 \, \alpha + 2 \, \beta\right)} + 11 \, k_{1}^{3} k_{2}^{4} e^{\left(2 \, \alpha + 2 \, \beta\right)} - 10 \, k_{1}^{2} k_{2}^{5} e^{\left(2 \, \alpha + 2 \, \beta\right)} - 4 \, k_{1} k_{2}^{6} e^{\left(2 \, \alpha + 2 \, \beta\right)} + 3 \, k_{2}^{7} e^{\left(2 \, \alpha + 2 \, \beta\right)}\right)} e^{\left(2 \, k_{1} x\right)} - {\left(3 \, k_{1}^{7} e^{\left(\alpha + 2 \, \beta\right)} + 4 \, k_{1}^{6} k_{2} e^{\left(\alpha + 2 \, \beta\right)} - 10 \, k_{1}^{5} k_{2}^{2} e^{\left(\alpha + 2 \, \beta\right)} - 11 \, k_{1}^{4} k_{2}^{3} e^{\left(\alpha + 2 \, \beta\right)} + 11 \, k_{1}^{3} k_{2}^{4} e^{\left(\alpha + 2 \, \beta\right)} + 10 \, k_{1}^{2} k_{2}^{5} e^{\left(\alpha + 2 \, \beta\right)} - 4 \, k_{1} k_{2}^{6} e^{\left(\alpha + 2 \, \beta\right)} - 3 \, k_{2}^{7} e^{\left(\alpha + 2 \, \beta\right)}\right)} e^{\left(k_{1} x\right)}\right)} e^{\left(2 \, k_{2} x\right)}}

\newcommand{\Bold}[1]{\mathbf{#1}}-\frac{{\left({\left(k_{1}^{11} e^{\left(\alpha + 3 \, \beta\right)} + c_{1} k_{1}^{9} e^{\left(\alpha + 3 \, \beta\right)} + {\left(k_{1}^{7} e^{\left(\alpha + 3 \, \beta\right)} + c_{1} k_{1}^{5} e^{\left(\alpha + 3 \, \beta\right)}\right)} k_{2}^{4} - 2 \, {\left(k_{1}^{9} e^{\left(\alpha + 3 \, \beta\right)} + c_{1} k_{1}^{7} e^{\left(\alpha + 3 \, \beta\right)}\right)} k_{2}^{2}\right)} e^{\left(k_{1} x\right)} - {\left(k_{1}^{11} e^{\left(2 \, \alpha + 3 \, \beta\right)} + c_{1} k_{1}^{9} e^{\left(2 \, \alpha + 3 \, \beta\right)} + {\left(k_{1}^{7} e^{\left(2 \, \alpha + 3 \, \beta\right)} + c_{1} k_{1}^{5} e^{\left(2 \, \alpha + 3 \, \beta\right)}\right)} k_{2}^{4} - 4 \, {\left(k_{1}^{8} e^{\left(2 \, \alpha + 3 \, \beta\right)} + c_{1} k_{1}^{6} e^{\left(2 \, \alpha + 3 \, \beta\right)}\right)} k_{2}^{3} + 6 \, {\left(k_{1}^{9} e^{\left(2 \, \alpha + 3 \, \beta\right)} + c_{1} k_{1}^{7} e^{\left(2 \, \alpha + 3 \, \beta\right)}\right)} k_{2}^{2} - 4 \, {\left(k_{1}^{10} e^{\left(2 \, \alpha + 3 \, \beta\right)} + c_{1} k_{1}^{8} e^{\left(2 \, \alpha + 3 \, \beta\right)}\right)} k_{2}\right)} e^{\left(2 \, k_{1} x\right)}\right)} e^{\left(3 \, k_{2} x\right)} + {\left(k_{1}^{11} e^{\alpha} + c_{1} k_{1}^{9} e^{\alpha} + {\left(k_{1}^{7} e^{\alpha} + c_{1} k_{1}^{5} e^{\alpha}\right)} k_{2}^{4} + 4 \, {\left(k_{1}^{8} e^{\alpha} + c_{1} k_{1}^{6} e^{\alpha}\right)} k_{2}^{3} + 6 \, {\left(k_{1}^{9} e^{\alpha} + c_{1} k_{1}^{7} e^{\alpha}\right)} k_{2}^{2} + 4 \, {\left(k_{1}^{10} e^{\alpha} + c_{1} k_{1}^{8} e^{\alpha}\right)} k_{2}\right)} e^{\left(k_{1} x\right)} - {\left(k_{1}^{11} e^{\left(2 \, \alpha\right)} + c_{1} k_{1}^{9} e^{\left(2 \, \alpha\right)} + {\left(k_{1}^{7} e^{\left(2 \, \alpha\right)} + c_{1} k_{1}^{5} e^{\left(2 \, \alpha\right)}\right)} k_{2}^{4} + 4 \, {\left(k_{1}^{8} e^{\left(2 \, \alpha\right)} + c_{1} k_{1}^{6} e^{\left(2 \, \alpha\right)}\right)} k_{2}^{3} + 6 \, {\left(k_{1}^{9} e^{\left(2 \, \alpha\right)} + c_{1} k_{1}^{7} e^{\left(2 \, \alpha\right)}\right)} k_{2}^{2} + 4 \, {\left(k_{1}^{10} e^{\left(2 \, \alpha\right)} + c_{1} k_{1}^{8} e^{\left(2 \, \alpha\right)}\right)} k_{2}\right)} e^{\left(2 \, k_{1} x\right)} + {\left(4 \, k_{1} k_{2}^{10} e^{\beta} + k_{2}^{11} e^{\beta} + c_{1} k_{1}^{4} k_{2}^{5} e^{\beta} + 4 \, c_{1} k_{1}^{3} k_{2}^{6} e^{\beta} + {\left(6 \, k_{1}^{2} e^{\beta} + c_{1} e^{\beta}\right)} k_{2}^{9} + 4 \, {\left(k_{1}^{3} e^{\beta} + c_{1} k_{1} e^{\beta}\right)} k_{2}^{8} + {\left(k_{1}^{4} e^{\beta} + 6 \, c_{1} k_{1}^{2} e^{\beta}\right)} k_{2}^{7} + {\left(k_{2}^{11} e^{\left(3 \, \alpha + \beta\right)} + c_{1} k_{1}^{4} k_{2}^{5} e^{\left(3 \, \alpha + \beta\right)} - {\left(2 \, k_{1}^{2} e^{\left(3 \, \alpha + \beta\right)} - c_{1} e^{\left(3 \, \alpha + \beta\right)}\right)} k_{2}^{9} + {\left(k_{1}^{4} e^{\left(3 \, \alpha + \beta\right)} - 2 \, c_{1} k_{1}^{2} e^{\left(3 \, \alpha + \beta\right)}\right)} k_{2}^{7}\right)} e^{\left(3 \, k_{1} x\right)} - {\left(3 \, k_{1}^{11} e^{\left(2 \, \alpha + \beta\right)} - 4 \, k_{1} k_{2}^{10} e^{\left(2 \, \alpha + \beta\right)} - 3 \, k_{2}^{11} e^{\left(2 \, \alpha + \beta\right)} + 3 \, c_{1} k_{1}^{9} e^{\left(2 \, \alpha + \beta\right)} + 3 \, {\left(2 \, k_{1}^{2} e^{\left(2 \, \alpha + \beta\right)} - c_{1} e^{\left(2 \, \alpha + \beta\right)}\right)} k_{2}^{9} + 4 \, {\left(2 \, k_{1}^{3} e^{\left(2 \, \alpha + \beta\right)} - c_{1} k_{1} e^{\left(2 \, \alpha + \beta\right)}\right)} k_{2}^{8} - 3 \, {\left(k_{1}^{4} e^{\left(2 \, \alpha + \beta\right)} - 2 \, c_{1} k_{1}^{2} e^{\left(2 \, \alpha + \beta\right)}\right)} k_{2}^{7} - 4 \, {\left(k_{1}^{5} e^{\left(2 \, \alpha + \beta\right)} - 2 \, c_{1} k_{1}^{3} e^{\left(2 \, \alpha + \beta\right)}\right)} k_{2}^{6} + {\left(4 \, k_{1}^{6} e^{\left(2 \, \alpha + \beta\right)} + c_{1} k_{1}^{4} e^{\left(2 \, \alpha + \beta\right)}\right)} k_{2}^{5} + {\left(3 \, k_{1}^{7} e^{\left(2 \, \alpha + \beta\right)} - c_{1} k_{1}^{5} e^{\left(2 \, \alpha + \beta\right)}\right)} k_{2}^{4} - 8 \, {\left(k_{1}^{8} e^{\left(2 \, \alpha + \beta\right)} + c_{1} k_{1}^{6} e^{\left(2 \, \alpha + \beta\right)}\right)} k_{2}^{3} - 6 \, {\left(k_{1}^{9} e^{\left(2 \, \alpha + \beta\right)} + c_{1} k_{1}^{7} e^{\left(2 \, \alpha + \beta\right)}\right)} k_{2}^{2} + 4 \, {\left(k_{1}^{10} e^{\left(2 \, \alpha + \beta\right)} + c_{1} k_{1}^{8} e^{\left(2 \, \alpha + \beta\right)}\right)} k_{2}\right)} e^{\left(2 \, k_{1} x\right)} + {\left(3 \, k_{1}^{11} e^{\left(\alpha + \beta\right)} + 8 \, k_{1} k_{2}^{10} e^{\left(\alpha + \beta\right)} + 3 \, k_{2}^{11} e^{\left(\alpha + \beta\right)} + 3 \, c_{1} k_{1}^{9} e^{\left(\alpha + \beta\right)} + {\left(2 \, k_{1}^{2} e^{\left(\alpha + \beta\right)} + 3 \, c_{1} e^{\left(\alpha + \beta\right)}\right)} k_{2}^{9} - 4 \, {\left(3 \, k_{1}^{3} e^{\left(\alpha + \beta\right)} - 2 \, c_{1} k_{1} e^{\left(\alpha + \beta\right)}\right)} k_{2}^{8} - {\left(13 \, k_{1}^{4} e^{\left(\alpha + \beta\right)} - 2 \, c_{1} k_{1}^{2} e^{\left(\alpha + \beta\right)}\right)} k_{2}^{7} - 4 \, {\left(k_{1}^{5} e^{\left(\alpha + \beta\right)} + 3 \, c_{1} k_{1}^{3} e^{\left(\alpha + \beta\right)}\right)} k_{2}^{6} - {\left(4 \, k_{1}^{6} e^{\left(\alpha + \beta\right)} + 17 \, c_{1} k_{1}^{4} e^{\left(\alpha + \beta\right)}\right)} k_{2}^{5} - {\left(13 \, k_{1}^{7} e^{\left(\alpha + \beta\right)} + 17 \, c_{1} k_{1}^{5} e^{\left(\alpha + \beta\right)}\right)} k_{2}^{4} - 12 \, {\left(k_{1}^{8} e^{\left(\alpha + \beta\right)} + c_{1} k_{1}^{6} e^{\left(\alpha + \beta\right)}\right)} k_{2}^{3} + 2 \, {\left(k_{1}^{9} e^{\left(\alpha + \beta\right)} + c_{1} k_{1}^{7} e^{\left(\alpha + \beta\right)}\right)} k_{2}^{2} + 8 \, {\left(k_{1}^{10} e^{\left(\alpha + \beta\right)} + c_{1} k_{1}^{8} e^{\left(\alpha + \beta\right)}\right)} k_{2}\right)} e^{\left(k_{1} x\right)}\right)} e^{\left(k_{2} x\right)} - {\left(4 \, k_{1} k_{2}^{10} e^{\left(2 \, \beta\right)} + k_{2}^{11} e^{\left(2 \, \beta\right)} + c_{1} k_{1}^{4} k_{2}^{5} e^{\left(2 \, \beta\right)} + 4 \, c_{1} k_{1}^{3} k_{2}^{6} e^{\left(2 \, \beta\right)} + {\left(6 \, k_{1}^{2} e^{\left(2 \, \beta\right)} + c_{1} e^{\left(2 \, \beta\right)}\right)} k_{2}^{9} + 4 \, {\left(k_{1}^{3} e^{\left(2 \, \beta\right)} + c_{1} k_{1} e^{\left(2 \, \beta\right)}\right)} k_{2}^{8} + {\left(k_{1}^{4} e^{\left(2 \, \beta\right)} + 6 \, c_{1} k_{1}^{2} e^{\left(2 \, \beta\right)}\right)} k_{2}^{7} - {\left(4 \, k_{1} k_{2}^{10} e^{\left(3 \, \alpha + 2 \, \beta\right)} - k_{2}^{11} e^{\left(3 \, \alpha + 2 \, \beta\right)} - c_{1} k_{1}^{4} k_{2}^{5} e^{\left(3 \, \alpha + 2 \, \beta\right)} + 4 \, c_{1} k_{1}^{3} k_{2}^{6} e^{\left(3 \, \alpha + 2 \, \beta\right)} - {\left(6 \, k_{1}^{2} e^{\left(3 \, \alpha + 2 \, \beta\right)} + c_{1} e^{\left(3 \, \alpha + 2 \, \beta\right)}\right)} k_{2}^{9} + 4 \, {\left(k_{1}^{3} e^{\left(3 \, \alpha + 2 \, \beta\right)} + c_{1} k_{1} e^{\left(3 \, \alpha + 2 \, \beta\right)}\right)} k_{2}^{8} - {\left(k_{1}^{4} e^{\left(3 \, \alpha + 2 \, \beta\right)} + 6 \, c_{1} k_{1}^{2} e^{\left(3 \, \alpha + 2 \, \beta\right)}\right)} k_{2}^{7}\right)} e^{\left(3 \, k_{1} x\right)} + {\left(3 \, k_{1}^{11} e^{\left(2 \, \alpha + 2 \, \beta\right)} - 4 \, k_{1} k_{2}^{10} e^{\left(2 \, \alpha + 2 \, \beta\right)} + 3 \, k_{2}^{11} e^{\left(2 \, \alpha + 2 \, \beta\right)} + 3 \, c_{1} k_{1}^{9} e^{\left(2 \, \alpha + 2 \, \beta\right)} - 3 \, {\left(2 \, k_{1}^{2} e^{\left(2 \, \alpha + 2 \, \beta\right)} - c_{1} e^{\left(2 \, \alpha + 2 \, \beta\right)}\right)} k_{2}^{9} + 4 \, {\left(2 \, k_{1}^{3} e^{\left(2 \, \alpha + 2 \, \beta\right)} - c_{1} k_{1} e^{\left(2 \, \alpha + 2 \, \beta\right)}\right)} k_{2}^{8} + 3 \, {\left(k_{1}^{4} e^{\left(2 \, \alpha + 2 \, \beta\right)} - 2 \, c_{1} k_{1}^{2} e^{\left(2 \, \alpha + 2 \, \beta\right)}\right)} k_{2}^{7} - 4 \, {\left(k_{1}^{5} e^{\left(2 \, \alpha + 2 \, \beta\right)} - 2 \, c_{1} k_{1}^{3} e^{\left(2 \, \alpha + 2 \, \beta\right)}\right)} k_{2}^{6} - {\left(4 \, k_{1}^{6} e^{\left(2 \, \alpha + 2 \, \beta\right)} + c_{1} k_{1}^{4} e^{\left(2 \, \alpha + 2 \, \beta\right)}\right)} k_{2}^{5} + {\left(3 \, k_{1}^{7} e^{\left(2 \, \alpha + 2 \, \beta\right)} - c_{1} k_{1}^{5} e^{\left(2 \, \alpha + 2 \, \beta\right)}\right)} k_{2}^{4} + 8 \, {\left(k_{1}^{8} e^{\left(2 \, \alpha + 2 \, \beta\right)} + c_{1} k_{1}^{6} e^{\left(2 \, \alpha + 2 \, \beta\right)}\right)} k_{2}^{3} - 6 \, {\left(k_{1}^{9} e^{\left(2 \, \alpha + 2 \, \beta\right)} + c_{1} k_{1}^{7} e^{\left(2 \, \alpha + 2 \, \beta\right)}\right)} k_{2}^{2} - 4 \, {\left(k_{1}^{10} e^{\left(2 \, \alpha + 2 \, \beta\right)} + c_{1} k_{1}^{8} e^{\left(2 \, \alpha + 2 \, \beta\right)}\right)} k_{2}\right)} e^{\left(2 \, k_{1} x\right)} - {\left(3 \, k_{1}^{11} e^{\left(\alpha + 2 \, \beta\right)} - 4 \, k_{1} k_{2}^{10} e^{\left(\alpha + 2 \, \beta\right)} - 3 \, k_{2}^{11} e^{\left(\alpha + 2 \, \beta\right)} + 3 \, c_{1} k_{1}^{9} e^{\left(\alpha + 2 \, \beta\right)} + 3 \, {\left(2 \, k_{1}^{2} e^{\left(\alpha + 2 \, \beta\right)} - c_{1} e^{\left(\alpha + 2 \, \beta\right)}\right)} k_{2}^{9} + 4 \, {\left(2 \, k_{1}^{3} e^{\left(\alpha + 2 \, \beta\right)} - c_{1} k_{1} e^{\left(\alpha + 2 \, \beta\right)}\right)} k_{2}^{8} - 3 \, {\left(k_{1}^{4} e^{\left(\alpha + 2 \, \beta\right)} - 2 \, c_{1} k_{1}^{2} e^{\left(\alpha + 2 \, \beta\right)}\right)} k_{2}^{7} - 4 \, {\left(k_{1}^{5} e^{\left(\alpha + 2 \, \beta\right)} - 2 \, c_{1} k_{1}^{3} e^{\left(\alpha + 2 \, \beta\right)}\right)} k_{2}^{6} + {\left(4 \, k_{1}^{6} e^{\left(\alpha + 2 \, \beta\right)} + c_{1} k_{1}^{4} e^{\left(\alpha + 2 \, \beta\right)}\right)} k_{2}^{5} + {\left(3 \, k_{1}^{7} e^{\left(\alpha + 2 \, \beta\right)} - c_{1} k_{1}^{5} e^{\left(\alpha + 2 \, \beta\right)}\right)} k_{2}^{4} - 8 \, {\left(k_{1}^{8} e^{\left(\alpha + 2 \, \beta\right)} + c_{1} k_{1}^{6} e^{\left(\alpha + 2 \, \beta\right)}\right)} k_{2}^{3} - 6 \, {\left(k_{1}^{9} e^{\left(\alpha + 2 \, \beta\right)} + c_{1} k_{1}^{7} e^{\left(\alpha + 2 \, \beta\right)}\right)} k_{2}^{2} + 4 \, {\left(k_{1}^{10} e^{\left(\alpha + 2 \, \beta\right)} + c_{1} k_{1}^{8} e^{\left(\alpha + 2 \, \beta\right)}\right)} k_{2}\right)} e^{\left(k_{1} x\right)}\right)} e^{\left(2 \, k_{2} x\right)}}{{\left({\left(k_{1}^{7} e^{\left(\alpha + 3 \, \beta\right)} - 2 \, k_{1}^{5} k_{2}^{2} e^{\left(\alpha + 3 \, \beta\right)} + k_{1}^{3} k_{2}^{4} e^{\left(\alpha + 3 \, \beta\right)}\right)} e^{\left(k_{1} x\right)} - {\left(k_{1}^{7} e^{\left(2 \, \alpha + 3 \, \beta\right)} - 4 \, k_{1}^{6} k_{2} e^{\left(2 \, \alpha + 3 \, \beta\right)} + 6 \, k_{1}^{5} k_{2}^{2} e^{\left(2 \, \alpha + 3 \, \beta\right)} - 4 \, k_{1}^{4} k_{2}^{3} e^{\left(2 \, \alpha + 3 \, \beta\right)} + k_{1}^{3} k_{2}^{4} e^{\left(2 \, \alpha + 3 \, \beta\right)}\right)} e^{\left(2 \, k_{1} x\right)}\right)} e^{\left(3 \, k_{2} x\right)} + {\left(k_{1}^{7} e^{\alpha} + 4 \, k_{1}^{6} k_{2} e^{\alpha} + 6 \, k_{1}^{5} k_{2}^{2} e^{\alpha} + 4 \, k_{1}^{4} k_{2}^{3} e^{\alpha} + k_{1}^{3} k_{2}^{4} e^{\alpha}\right)} e^{\left(k_{1} x\right)} - {\left(k_{1}^{7} e^{\left(2 \, \alpha\right)} + 4 \, k_{1}^{6} k_{2} e^{\left(2 \, \alpha\right)} + 6 \, k_{1}^{5} k_{2}^{2} e^{\left(2 \, \alpha\right)} + 4 \, k_{1}^{4} k_{2}^{3} e^{\left(2 \, \alpha\right)} + k_{1}^{3} k_{2}^{4} e^{\left(2 \, \alpha\right)}\right)} e^{\left(2 \, k_{1} x\right)} + {\left(k_{1}^{4} k_{2}^{3} e^{\beta} + 4 \, k_{1}^{3} k_{2}^{4} e^{\beta} + 6 \, k_{1}^{2} k_{2}^{5} e^{\beta} + 4 \, k_{1} k_{2}^{6} e^{\beta} + k_{2}^{7} e^{\beta} + {\left(k_{1}^{4} k_{2}^{3} e^{\left(3 \, \alpha + \beta\right)} - 2 \, k_{1}^{2} k_{2}^{5} e^{\left(3 \, \alpha + \beta\right)} + k_{2}^{7} e^{\left(3 \, \alpha + \beta\right)}\right)} e^{\left(3 \, k_{1} x\right)} - {\left(3 \, k_{1}^{7} e^{\left(2 \, \alpha + \beta\right)} + 4 \, k_{1}^{6} k_{2} e^{\left(2 \, \alpha + \beta\right)} - 10 \, k_{1}^{5} k_{2}^{2} e^{\left(2 \, \alpha + \beta\right)} - 11 \, k_{1}^{4} k_{2}^{3} e^{\left(2 \, \alpha + \beta\right)} + 11 \, k_{1}^{3} k_{2}^{4} e^{\left(2 \, \alpha + \beta\right)} + 10 \, k_{1}^{2} k_{2}^{5} e^{\left(2 \, \alpha + \beta\right)} - 4 \, k_{1} k_{2}^{6} e^{\left(2 \, \alpha + \beta\right)} - 3 \, k_{2}^{7} e^{\left(2 \, \alpha + \beta\right)}\right)} e^{\left(2 \, k_{1} x\right)} + {\left(3 \, k_{1}^{7} e^{\left(\alpha + \beta\right)} + 8 \, k_{1}^{6} k_{2} e^{\left(\alpha + \beta\right)} - 2 \, k_{1}^{5} k_{2}^{2} e^{\left(\alpha + \beta\right)} - 25 \, k_{1}^{4} k_{2}^{3} e^{\left(\alpha + \beta\right)} - 25 \, k_{1}^{3} k_{2}^{4} e^{\left(\alpha + \beta\right)} - 2 \, k_{1}^{2} k_{2}^{5} e^{\left(\alpha + \beta\right)} + 8 \, k_{1} k_{2}^{6} e^{\left(\alpha + \beta\right)} + 3 \, k_{2}^{7} e^{\left(\alpha + \beta\right)}\right)} e^{\left(k_{1} x\right)}\right)} e^{\left(k_{2} x\right)} - {\left(k_{1}^{4} k_{2}^{3} e^{\left(2 \, \beta\right)} + 4 \, k_{1}^{3} k_{2}^{4} e^{\left(2 \, \beta\right)} + 6 \, k_{1}^{2} k_{2}^{5} e^{\left(2 \, \beta\right)} + 4 \, k_{1} k_{2}^{6} e^{\left(2 \, \beta\right)} + k_{2}^{7} e^{\left(2 \, \beta\right)} + {\left(k_{1}^{4} k_{2}^{3} e^{\left(3 \, \alpha + 2 \, \beta\right)} - 4 \, k_{1}^{3} k_{2}^{4} e^{\left(3 \, \alpha + 2 \, \beta\right)} + 6 \, k_{1}^{2} k_{2}^{5} e^{\left(3 \, \alpha + 2 \, \beta\right)} - 4 \, k_{1} k_{2}^{6} e^{\left(3 \, \alpha + 2 \, \beta\right)} + k_{2}^{7} e^{\left(3 \, \alpha + 2 \, \beta\right)}\right)} e^{\left(3 \, k_{1} x\right)} + {\left(3 \, k_{1}^{7} e^{\left(2 \, \alpha + 2 \, \beta\right)} - 4 \, k_{1}^{6} k_{2} e^{\left(2 \, \alpha + 2 \, \beta\right)} - 10 \, k_{1}^{5} k_{2}^{2} e^{\left(2 \, \alpha + 2 \, \beta\right)} + 11 \, k_{1}^{4} k_{2}^{3} e^{\left(2 \, \alpha + 2 \, \beta\right)} + 11 \, k_{1}^{3} k_{2}^{4} e^{\left(2 \, \alpha + 2 \, \beta\right)} - 10 \, k_{1}^{2} k_{2}^{5} e^{\left(2 \, \alpha + 2 \, \beta\right)} - 4 \, k_{1} k_{2}^{6} e^{\left(2 \, \alpha + 2 \, \beta\right)} + 3 \, k_{2}^{7} e^{\left(2 \, \alpha + 2 \, \beta\right)}\right)} e^{\left(2 \, k_{1} x\right)} - {\left(3 \, k_{1}^{7} e^{\left(\alpha + 2 \, \beta\right)} + 4 \, k_{1}^{6} k_{2} e^{\left(\alpha + 2 \, \beta\right)} - 10 \, k_{1}^{5} k_{2}^{2} e^{\left(\alpha + 2 \, \beta\right)} - 11 \, k_{1}^{4} k_{2}^{3} e^{\left(\alpha + 2 \, \beta\right)} + 11 \, k_{1}^{3} k_{2}^{4} e^{\left(\alpha + 2 \, \beta\right)} + 10 \, k_{1}^{2} k_{2}^{5} e^{\left(\alpha + 2 \, \beta\right)} - 4 \, k_{1} k_{2}^{6} e^{\left(\alpha + 2 \, \beta\right)} - 3 \, k_{2}^{7} e^{\left(\alpha + 2 \, \beta\right)}\right)} e^{\left(k_{1} x\right)}\right)} e^{\left(2 \, k_{2} x\right)}}

dzero = solve([bigeqn(alpha=0,beta=0)==0], c_0, c_1, solution_dict=True)[0][0]

show(dzero[c_0].simplify_full())

\newcommand{\Bold}[1]{\mathbf{#1}}-\frac{{\left({\left(k_{1}^{11} + c_{1} k_{1}^{9} + {\left(k_{1}^{7} + c_{1} k_{1}^{5}\right)} k_{2}^{4} - 2 \, {\left(k_{1}^{9} + c_{1} k_{1}^{7}\right)} k_{2}^{2}\right)} e^{\left(k_{1} x\right)} - {\left(k_{1}^{11} + c_{1} k_{1}^{9} + {\left(k_{1}^{7} + c_{1} k_{1}^{5}\right)} k_{2}^{4} - 4 \, {\left(k_{1}^{8} + c_{1} k_{1}^{6}\right)} k_{2}^{3} + 6 \, {\left(k_{1}^{9} + c_{1} k_{1}^{7}\right)} k_{2}^{2} - 4 \, {\left(k_{1}^{10} + c_{1} k_{1}^{8}\right)} k_{2}\right)} e^{\left(2 \, k_{1} x\right)}\right)} e^{\left(3 \, k_{2} x\right)} + {\left(k_{1}^{11} + c_{1} k_{1}^{9} + {\left(k_{1}^{7} + c_{1} k_{1}^{5}\right)} k_{2}^{4} + 4 \, {\left(k_{1}^{8} + c_{1} k_{1}^{6}\right)} k_{2}^{3} + 6 \, {\left(k_{1}^{9} + c_{1} k_{1}^{7}\right)} k_{2}^{2} + 4 \, {\left(k_{1}^{10} + c_{1} k_{1}^{8}\right)} k_{2}\right)} e^{\left(k_{1} x\right)} - {\left(k_{1}^{11} + c_{1} k_{1}^{9} + {\left(k_{1}^{7} + c_{1} k_{1}^{5}\right)} k_{2}^{4} + 4 \, {\left(k_{1}^{8} + c_{1} k_{1}^{6}\right)} k_{2}^{3} + 6 \, {\left(k_{1}^{9} + c_{1} k_{1}^{7}\right)} k_{2}^{2} + 4 \, {\left(k_{1}^{10} + c_{1} k_{1}^{8}\right)} k_{2}\right)} e^{\left(2 \, k_{1} x\right)} - {\left(4 \, k_{1} k_{2}^{10} + k_{2}^{11} + {\left(6 \, k_{1}^{2} + c_{1}\right)} k_{2}^{9} + c_{1} k_{1}^{4} k_{2}^{5} + 4 \, c_{1} k_{1}^{3} k_{2}^{6} + 4 \, {\left(k_{1}^{3} + c_{1} k_{1}\right)} k_{2}^{8} + {\left(k_{1}^{4} + 6 \, c_{1} k_{1}^{2}\right)} k_{2}^{7} - {\left(4 \, k_{1} k_{2}^{10} - k_{2}^{11} - {\left(6 \, k_{1}^{2} + c_{1}\right)} k_{2}^{9} - c_{1} k_{1}^{4} k_{2}^{5} + 4 \, c_{1} k_{1}^{3} k_{2}^{6} + 4 \, {\left(k_{1}^{3} + c_{1} k_{1}\right)} k_{2}^{8} - {\left(k_{1}^{4} + 6 \, c_{1} k_{1}^{2}\right)} k_{2}^{7}\right)} e^{\left(3 \, k_{1} x\right)} - {\left(3 \, k_{1}^{11} - 4 \, k_{1} k_{2}^{10} - 3 \, k_{2}^{11} + 3 \, {\left(2 \, k_{1}^{2} - c_{1}\right)} k_{2}^{9} + 3 \, c_{1} k_{1}^{9} + 4 \, {\left(2 \, k_{1}^{3} - c_{1} k_{1}\right)} k_{2}^{8} - 3 \, {\left(k_{1}^{4} - 2 \, c_{1} k_{1}^{2}\right)} k_{2}^{7} - 4 \, {\left(k_{1}^{5} - 2 \, c_{1} k_{1}^{3}\right)} k_{2}^{6} + {\left(4 \, k_{1}^{6} + c_{1} k_{1}^{4}\right)} k_{2}^{5} + {\left(3 \, k_{1}^{7} - c_{1} k_{1}^{5}\right)} k_{2}^{4} - 8 \, {\left(k_{1}^{8} + c_{1} k_{1}^{6}\right)} k_{2}^{3} - 6 \, {\left(k_{1}^{9} + c_{1} k_{1}^{7}\right)} k_{2}^{2} + 4 \, {\left(k_{1}^{10} + c_{1} k_{1}^{8}\right)} k_{2}\right)} e^{\left(k_{1} x\right)} + {\left(3 \, k_{1}^{11} - 4 \, k_{1} k_{2}^{10} + 3 \, k_{2}^{11} - 3 \, {\left(2 \, k_{1}^{2} - c_{1}\right)} k_{2}^{9} + 3 \, c_{1} k_{1}^{9} + 4 \, {\left(2 \, k_{1}^{3} - c_{1} k_{1}\right)} k_{2}^{8} + 3 \, {\left(k_{1}^{4} - 2 \, c_{1} k_{1}^{2}\right)} k_{2}^{7} - 4 \, {\left(k_{1}^{5} - 2 \, c_{1} k_{1}^{3}\right)} k_{2}^{6} - {\left(4 \, k_{1}^{6} + c_{1} k_{1}^{4}\right)} k_{2}^{5} + {\left(3 \, k_{1}^{7} - c_{1} k_{1}^{5}\right)} k_{2}^{4} + 8 \, {\left(k_{1}^{8} + c_{1} k_{1}^{6}\right)} k_{2}^{3} - 6 \, {\left(k_{1}^{9} + c_{1} k_{1}^{7}\right)} k_{2}^{2} - 4 \, {\left(k_{1}^{10} + c_{1} k_{1}^{8}\right)} k_{2}\right)} e^{\left(2 \, k_{1} x\right)}\right)} e^{\left(2 \, k_{2} x\right)} + {\left(4 \, k_{1} k_{2}^{10} + k_{2}^{11} + {\left(6 \, k_{1}^{2} + c_{1}\right)} k_{2}^{9} + c_{1} k_{1}^{4} k_{2}^{5} + 4 \, c_{1} k_{1}^{3} k_{2}^{6} + 4 \, {\left(k_{1}^{3} + c_{1} k_{1}\right)} k_{2}^{8} + {\left(k_{1}^{4} + 6 \, c_{1} k_{1}^{2}\right)} k_{2}^{7} + {\left(k_{2}^{11} - {\left(2 \, k_{1}^{2} - c_{1}\right)} k_{2}^{9} + c_{1} k_{1}^{4} k_{2}^{5} + {\left(k_{1}^{4} - 2 \, c_{1} k_{1}^{2}\right)} k_{2}^{7}\right)} e^{\left(3 \, k_{1} x\right)} - {\left(3 \, k_{1}^{11} - 4 \, k_{1} k_{2}^{10} - 3 \, k_{2}^{11} + 3 \, {\left(2 \, k_{1}^{2} - c_{1}\right)} k_{2}^{9} + 3 \, c_{1} k_{1}^{9} + 4 \, {\left(2 \, k_{1}^{3} - c_{1} k_{1}\right)} k_{2}^{8} - 3 \, {\left(k_{1}^{4} - 2 \, c_{1} k_{1}^{2}\right)} k_{2}^{7} - 4 \, {\left(k_{1}^{5} - 2 \, c_{1} k_{1}^{3}\right)} k_{2}^{6} + {\left(4 \, k_{1}^{6} + c_{1} k_{1}^{4}\right)} k_{2}^{5} + {\left(3 \, k_{1}^{7} - c_{1} k_{1}^{5}\right)} k_{2}^{4} - 8 \, {\left(k_{1}^{8} + c_{1} k_{1}^{6}\right)} k_{2}^{3} - 6 \, {\left(k_{1}^{9} + c_{1} k_{1}^{7}\right)} k_{2}^{2} + 4 \, {\left(k_{1}^{10} + c_{1} k_{1}^{8}\right)} k_{2}\right)} e^{\left(2 \, k_{1} x\right)} + {\left(3 \, k_{1}^{11} + 8 \, k_{1} k_{2}^{10} + 3 \, k_{2}^{11} + {\left(2 \, k_{1}^{2} + 3 \, c_{1}\right)} k_{2}^{9} + 3 \, c_{1} k_{1}^{9} - 4 \, {\left(3 \, k_{1}^{3} - 2 \, c_{1} k_{1}\right)} k_{2}^{8} - {\left(13 \, k_{1}^{4} - 2 \, c_{1} k_{1}^{2}\right)} k_{2}^{7} - 4 \, {\left(k_{1}^{5} + 3 \, c_{1} k_{1}^{3}\right)} k_{2}^{6} - {\left(4 \, k_{1}^{6} + 17 \, c_{1} k_{1}^{4}\right)} k_{2}^{5} - {\left(13 \, k_{1}^{7} + 17 \, c_{1} k_{1}^{5}\right)} k_{2}^{4} - 12 \, {\left(k_{1}^{8} + c_{1} k_{1}^{6}\right)} k_{2}^{3} + 2 \, {\left(k_{1}^{9} + c_{1} k_{1}^{7}\right)} k_{2}^{2} + 8 \, {\left(k_{1}^{10} + c_{1} k_{1}^{8}\right)} k_{2}\right)} e^{\left(k_{1} x\right)}\right)} e^{\left(k_{2} x\right)}}{{\left({\left(k_{1}^{7} - 2 \, k_{1}^{5} k_{2}^{2} + k_{1}^{3} k_{2}^{4}\right)} e^{\left(k_{1} x\right)} - {\left(k_{1}^{7} - 4 \, k_{1}^{6} k_{2} + 6 \, k_{1}^{5} k_{2}^{2} - 4 \, k_{1}^{4} k_{2}^{3} + k_{1}^{3} k_{2}^{4}\right)} e^{\left(2 \, k_{1} x\right)}\right)} e^{\left(3 \, k_{2} x\right)} + {\left(k_{1}^{7} + 4 \, k_{1}^{6} k_{2} + 6 \, k_{1}^{5} k_{2}^{2} + 4 \, k_{1}^{4} k_{2}^{3} + k_{1}^{3} k_{2}^{4}\right)} e^{\left(k_{1} x\right)} - {\left(k_{1}^{7} + 4 \, k_{1}^{6} k_{2} + 6 \, k_{1}^{5} k_{2}^{2} + 4 \, k_{1}^{4} k_{2}^{3} + k_{1}^{3} k_{2}^{4}\right)} e^{\left(2 \, k_{1} x\right)} - {\left(k_{1}^{4} k_{2}^{3} + 4 \, k_{1}^{3} k_{2}^{4} + 6 \, k_{1}^{2} k_{2}^{5} + 4 \, k_{1} k_{2}^{6} + k_{2}^{7} + {\left(k_{1}^{4} k_{2}^{3} - 4 \, k_{1}^{3} k_{2}^{4} + 6 \, k_{1}^{2} k_{2}^{5} - 4 \, k_{1} k_{2}^{6} + k_{2}^{7}\right)} e^{\left(3 \, k_{1} x\right)} + {\left(3 \, k_{1}^{7} - 4 \, k_{1}^{6} k_{2} - 10 \, k_{1}^{5} k_{2}^{2} + 11 \, k_{1}^{4} k_{2}^{3} + 11 \, k_{1}^{3} k_{2}^{4} - 10 \, k_{1}^{2} k_{2}^{5} - 4 \, k_{1} k_{2}^{6} + 3 \, k_{2}^{7}\right)} e^{\left(2 \, k_{1} x\right)} - {\left(3 \, k_{1}^{7} + 4 \, k_{1}^{6} k_{2} - 10 \, k_{1}^{5} k_{2}^{2} - 11 \, k_{1}^{4} k_{2}^{3} + 11 \, k_{1}^{3} k_{2}^{4} + 10 \, k_{1}^{2} k_{2}^{5} - 4 \, k_{1} k_{2}^{6} - 3 \, k_{2}^{7}\right)} e^{\left(k_{1} x\right)}\right)} e^{\left(2 \, k_{2} x\right)} + {\left(k_{1}^{4} k_{2}^{3} + 4 \, k_{1}^{3} k_{2}^{4} + 6 \, k_{1}^{2} k_{2}^{5} + 4 \, k_{1} k_{2}^{6} + k_{2}^{7} + {\left(k_{1}^{4} k_{2}^{3} - 2 \, k_{1}^{2} k_{2}^{5} + k_{2}^{7}\right)} e^{\left(3 \, k_{1} x\right)} - {\left(3 \, k_{1}^{7} + 4 \, k_{1}^{6} k_{2} - 10 \, k_{1}^{5} k_{2}^{2} - 11 \, k_{1}^{4} k_{2}^{3} + 11 \, k_{1}^{3} k_{2}^{4} + 10 \, k_{1}^{2} k_{2}^{5} - 4 \, k_{1} k_{2}^{6} - 3 \, k_{2}^{7}\right)} e^{\left(2 \, k_{1} x\right)} + {\left(3 \, k_{1}^{7} + 8 \, k_{1}^{6} k_{2} - 2 \, k_{1}^{5} k_{2}^{2} - 25 \, k_{1}^{4} k_{2}^{3} - 25 \, k_{1}^{3} k_{2}^{4} - 2 \, k_{1}^{2} k_{2}^{5} + 8 \, k_{1} k_{2}^{6} + 3 \, k_{2}^{7}\right)} e^{\left(k_{1} x\right)}\right)} e^{\left(k_{2} x\right)}}

\newcommand{\Bold}[1]{\mathbf{#1}}-\frac{{\left({\left(k_{1}^{11} + c_{1} k_{1}^{9} + {\left(k_{1}^{7} + c_{1} k_{1}^{5}\right)} k_{2}^{4} - 2 \, {\left(k_{1}^{9} + c_{1} k_{1}^{7}\right)} k_{2}^{2}\right)} e^{\left(k_{1} x\right)} - {\left(k_{1}^{11} + c_{1} k_{1}^{9} + {\left(k_{1}^{7} + c_{1} k_{1}^{5}\right)} k_{2}^{4} - 4 \, {\left(k_{1}^{8} + c_{1} k_{1}^{6}\right)} k_{2}^{3} + 6 \, {\left(k_{1}^{9} + c_{1} k_{1}^{7}\right)} k_{2}^{2} - 4 \, {\left(k_{1}^{10} + c_{1} k_{1}^{8}\right)} k_{2}\right)} e^{\left(2 \, k_{1} x\right)}\right)} e^{\left(3 \, k_{2} x\right)} + {\left(k_{1}^{11} + c_{1} k_{1}^{9} + {\left(k_{1}^{7} + c_{1} k_{1}^{5}\right)} k_{2}^{4} + 4 \, {\left(k_{1}^{8} + c_{1} k_{1}^{6}\right)} k_{2}^{3} + 6 \, {\left(k_{1}^{9} + c_{1} k_{1}^{7}\right)} k_{2}^{2} + 4 \, {\left(k_{1}^{10} + c_{1} k_{1}^{8}\right)} k_{2}\right)} e^{\left(k_{1} x\right)} - {\left(k_{1}^{11} + c_{1} k_{1}^{9} + {\left(k_{1}^{7} + c_{1} k_{1}^{5}\right)} k_{2}^{4} + 4 \, {\left(k_{1}^{8} + c_{1} k_{1}^{6}\right)} k_{2}^{3} + 6 \, {\left(k_{1}^{9} + c_{1} k_{1}^{7}\right)} k_{2}^{2} + 4 \, {\left(k_{1}^{10} + c_{1} k_{1}^{8}\right)} k_{2}\right)} e^{\left(2 \, k_{1} x\right)} - {\left(4 \, k_{1} k_{2}^{10} + k_{2}^{11} + {\left(6 \, k_{1}^{2} + c_{1}\right)} k_{2}^{9} + c_{1} k_{1}^{4} k_{2}^{5} + 4 \, c_{1} k_{1}^{3} k_{2}^{6} + 4 \, {\left(k_{1}^{3} + c_{1} k_{1}\right)} k_{2}^{8} + {\left(k_{1}^{4} + 6 \, c_{1} k_{1}^{2}\right)} k_{2}^{7} - {\left(4 \, k_{1} k_{2}^{10} - k_{2}^{11} - {\left(6 \, k_{1}^{2} + c_{1}\right)} k_{2}^{9} - c_{1} k_{1}^{4} k_{2}^{5} + 4 \, c_{1} k_{1}^{3} k_{2}^{6} + 4 \, {\left(k_{1}^{3} + c_{1} k_{1}\right)} k_{2}^{8} - {\left(k_{1}^{4} + 6 \, c_{1} k_{1}^{2}\right)} k_{2}^{7}\right)} e^{\left(3 \, k_{1} x\right)} - {\left(3 \, k_{1}^{11} - 4 \, k_{1} k_{2}^{10} - 3 \, k_{2}^{11} + 3 \, {\left(2 \, k_{1}^{2} - c_{1}\right)} k_{2}^{9} + 3 \, c_{1} k_{1}^{9} + 4 \, {\left(2 \, k_{1}^{3} - c_{1} k_{1}\right)} k_{2}^{8} - 3 \, {\left(k_{1}^{4} - 2 \, c_{1} k_{1}^{2}\right)} k_{2}^{7} - 4 \, {\left(k_{1}^{5} - 2 \, c_{1} k_{1}^{3}\right)} k_{2}^{6} + {\left(4 \, k_{1}^{6} + c_{1} k_{1}^{4}\right)} k_{2}^{5} + {\left(3 \, k_{1}^{7} - c_{1} k_{1}^{5}\right)} k_{2}^{4} - 8 \, {\left(k_{1}^{8} + c_{1} k_{1}^{6}\right)} k_{2}^{3} - 6 \, {\left(k_{1}^{9} + c_{1} k_{1}^{7}\right)} k_{2}^{2} + 4 \, {\left(k_{1}^{10} + c_{1} k_{1}^{8}\right)} k_{2}\right)} e^{\left(k_{1} x\right)} + {\left(3 \, k_{1}^{11} - 4 \, k_{1} k_{2}^{10} + 3 \, k_{2}^{11} - 3 \, {\left(2 \, k_{1}^{2} - c_{1}\right)} k_{2}^{9} + 3 \, c_{1} k_{1}^{9} + 4 \, {\left(2 \, k_{1}^{3} - c_{1} k_{1}\right)} k_{2}^{8} + 3 \, {\left(k_{1}^{4} - 2 \, c_{1} k_{1}^{2}\right)} k_{2}^{7} - 4 \, {\left(k_{1}^{5} - 2 \, c_{1} k_{1}^{3}\right)} k_{2}^{6} - {\left(4 \, k_{1}^{6} + c_{1} k_{1}^{4}\right)} k_{2}^{5} + {\left(3 \, k_{1}^{7} - c_{1} k_{1}^{5}\right)} k_{2}^{4} + 8 \, {\left(k_{1}^{8} + c_{1} k_{1}^{6}\right)} k_{2}^{3} - 6 \, {\left(k_{1}^{9} + c_{1} k_{1}^{7}\right)} k_{2}^{2} - 4 \, {\left(k_{1}^{10} + c_{1} k_{1}^{8}\right)} k_{2}\right)} e^{\left(2 \, k_{1} x\right)}\right)} e^{\left(2 \, k_{2} x\right)} + {\left(4 \, k_{1} k_{2}^{10} + k_{2}^{11} + {\left(6 \, k_{1}^{2} + c_{1}\right)} k_{2}^{9} + c_{1} k_{1}^{4} k_{2}^{5} + 4 \, c_{1} k_{1}^{3} k_{2}^{6} + 4 \, {\left(k_{1}^{3} + c_{1} k_{1}\right)} k_{2}^{8} + {\left(k_{1}^{4} + 6 \, c_{1} k_{1}^{2}\right)} k_{2}^{7} + {\left(k_{2}^{11} - {\left(2 \, k_{1}^{2} - c_{1}\right)} k_{2}^{9} + c_{1} k_{1}^{4} k_{2}^{5} + {\left(k_{1}^{4} - 2 \, c_{1} k_{1}^{2}\right)} k_{2}^{7}\right)} e^{\left(3 \, k_{1} x\right)} - {\left(3 \, k_{1}^{11} - 4 \, k_{1} k_{2}^{10} - 3 \, k_{2}^{11} + 3 \, {\left(2 \, k_{1}^{2} - c_{1}\right)} k_{2}^{9} + 3 \, c_{1} k_{1}^{9} + 4 \, {\left(2 \, k_{1}^{3} - c_{1} k_{1}\right)} k_{2}^{8} - 3 \, {\left(k_{1}^{4} - 2 \, c_{1} k_{1}^{2}\right)} k_{2}^{7} - 4 \, {\left(k_{1}^{5} - 2 \, c_{1} k_{1}^{3}\right)} k_{2}^{6} + {\left(4 \, k_{1}^{6} + c_{1} k_{1}^{4}\right)} k_{2}^{5} + {\left(3 \, k_{1}^{7} - c_{1} k_{1}^{5}\right)} k_{2}^{4} - 8 \, {\left(k_{1}^{8} + c_{1} k_{1}^{6}\right)} k_{2}^{3} - 6 \, {\left(k_{1}^{9} + c_{1} k_{1}^{7}\right)} k_{2}^{2} + 4 \, {\left(k_{1}^{10} + c_{1} k_{1}^{8}\right)} k_{2}\right)} e^{\left(2 \, k_{1} x\right)} + {\left(3 \, k_{1}^{11} + 8 \, k_{1} k_{2}^{10} + 3 \, k_{2}^{11} + {\left(2 \, k_{1}^{2} + 3 \, c_{1}\right)} k_{2}^{9} + 3 \, c_{1} k_{1}^{9} - 4 \, {\left(3 \, k_{1}^{3} - 2 \, c_{1} k_{1}\right)} k_{2}^{8} - {\left(13 \, k_{1}^{4} - 2 \, c_{1} k_{1}^{2}\right)} k_{2}^{7} - 4 \, {\left(k_{1}^{5} + 3 \, c_{1} k_{1}^{3}\right)} k_{2}^{6} - {\left(4 \, k_{1}^{6} + 17 \, c_{1} k_{1}^{4}\right)} k_{2}^{5} - {\left(13 \, k_{1}^{7} + 17 \, c_{1} k_{1}^{5}\right)} k_{2}^{4} - 12 \, {\left(k_{1}^{8} + c_{1} k_{1}^{6}\right)} k_{2}^{3} + 2 \, {\left(k_{1}^{9} + c_{1} k_{1}^{7}\right)} k_{2}^{2} + 8 \, {\left(k_{1}^{10} + c_{1} k_{1}^{8}\right)} k_{2}\right)} e^{\left(k_{1} x\right)}\right)} e^{\left(k_{2} x\right)}}{{\left({\left(k_{1}^{7} - 2 \, k_{1}^{5} k_{2}^{2} + k_{1}^{3} k_{2}^{4}\right)} e^{\left(k_{1} x\right)} - {\left(k_{1}^{7} - 4 \, k_{1}^{6} k_{2} + 6 \, k_{1}^{5} k_{2}^{2} - 4 \, k_{1}^{4} k_{2}^{3} + k_{1}^{3} k_{2}^{4}\right)} e^{\left(2 \, k_{1} x\right)}\right)} e^{\left(3 \, k_{2} x\right)} + {\left(k_{1}^{7} + 4 \, k_{1}^{6} k_{2} + 6 \, k_{1}^{5} k_{2}^{2} + 4 \, k_{1}^{4} k_{2}^{3} + k_{1}^{3} k_{2}^{4}\right)} e^{\left(k_{1} x\right)} - {\left(k_{1}^{7} + 4 \, k_{1}^{6} k_{2} + 6 \, k_{1}^{5} k_{2}^{2} + 4 \, k_{1}^{4} k_{2}^{3} + k_{1}^{3} k_{2}^{4}\right)} e^{\left(2 \, k_{1} x\right)} - {\left(k_{1}^{4} k_{2}^{3} + 4 \, k_{1}^{3} k_{2}^{4} + 6 \, k_{1}^{2} k_{2}^{5} + 4 \, k_{1} k_{2}^{6} + k_{2}^{7} + {\left(k_{1}^{4} k_{2}^{3} - 4 \, k_{1}^{3} k_{2}^{4} + 6 \, k_{1}^{2} k_{2}^{5} - 4 \, k_{1} k_{2}^{6} + k_{2}^{7}\right)} e^{\left(3 \, k_{1} x\right)} + {\left(3 \, k_{1}^{7} - 4 \, k_{1}^{6} k_{2} - 10 \, k_{1}^{5} k_{2}^{2} + 11 \, k_{1}^{4} k_{2}^{3} + 11 \, k_{1}^{3} k_{2}^{4} - 10 \, k_{1}^{2} k_{2}^{5} - 4 \, k_{1} k_{2}^{6} + 3 \, k_{2}^{7}\right)} e^{\left(2 \, k_{1} x\right)} - {\left(3 \, k_{1}^{7} + 4 \, k_{1}^{6} k_{2} - 10 \, k_{1}^{5} k_{2}^{2} - 11 \, k_{1}^{4} k_{2}^{3} + 11 \, k_{1}^{3} k_{2}^{4} + 10 \, k_{1}^{2} k_{2}^{5} - 4 \, k_{1} k_{2}^{6} - 3 \, k_{2}^{7}\right)} e^{\left(k_{1} x\right)}\right)} e^{\left(2 \, k_{2} x\right)} + {\left(k_{1}^{4} k_{2}^{3} + 4 \, k_{1}^{3} k_{2}^{4} + 6 \, k_{1}^{2} k_{2}^{5} + 4 \, k_{1} k_{2}^{6} + k_{2}^{7} + {\left(k_{1}^{4} k_{2}^{3} - 2 \, k_{1}^{2} k_{2}^{5} + k_{2}^{7}\right)} e^{\left(3 \, k_{1} x\right)} - {\left(3 \, k_{1}^{7} + 4 \, k_{1}^{6} k_{2} - 10 \, k_{1}^{5} k_{2}^{2} - 11 \, k_{1}^{4} k_{2}^{3} + 11 \, k_{1}^{3} k_{2}^{4} + 10 \, k_{1}^{2} k_{2}^{5} - 4 \, k_{1} k_{2}^{6} - 3 \, k_{2}^{7}\right)} e^{\left(2 \, k_{1} x\right)} + {\left(3 \, k_{1}^{7} + 8 \, k_{1}^{6} k_{2} - 2 \, k_{1}^{5} k_{2}^{2} - 25 \, k_{1}^{4} k_{2}^{3} - 25 \, k_{1}^{3} k_{2}^{4} - 2 \, k_{1}^{2} k_{2}^{5} + 8 \, k_{1} k_{2}^{6} + 3 \, k_{2}^{7}\right)} e^{\left(k_{1} x\right)}\right)} e^{\left(k_{2} x\right)}}

# # Heirarchy computations # var('x,t1,t2,t3,k_1,k_2') alpha = function('alpha',x,t1,t2,t3) beta = function('beta',x,t1,t2,t3) V = log(1 + exp(k_1*x + alpha) + exp(k_2*x + beta) + (k_1-k_2)^2/(k_1+k_2)^2 * exp(k_1*x + k_2*x + alpha + beta)) U = 2*V.derivative(x,2) Ux = diff(U,x) Uxx = diff(Ux,x) Uxxx = diff(Uxx,x) Uxxxx = diff(Uxxx,x) Uxxxxx = diff(Uxxxx,x) Ut1 = diff(U,t1).simplify_full() RHSt1 = (6*U*Ux + Uxxx).simplify_full()

Ut3 = diff(U,t3).simplify_full() RHSt3 = (140*U^3*Ux + 70*Ux^3 + 280*U*Ux*U_xx + 70*Uxx*Uxxx + 70*U^2*Uxxx + 42*Ux*Uxxxx + 14*U*Uxxxxx + U.derivative(x,7)).simplify_full()

Ut1.numerator()

WARNING: Output truncated!  
full_output.txt



\newcommand{\Bold}[1]{\mathbf{#1}}-2 \, {\left({\left({\left(3 \, k_{1}^{6} + 10 \, k_{1}^{5} k_{2} + 13 \, k_{1}^{4} k_{2}^{2} + 12 \, k_{1}^{3} k_{2}^{3} + 13 \, k_{1}^{2} k_{2}^{4} + 10 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(2 \, k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(3 \, k_{1}^{6} + 14 \, k_{1}^{5} k_{2} + 29 \, k_{1}^{4} k_{2}^{2} + 36 \, k_{1}^{3} k_{2}^{3} + 29 \, k_{1}^{2} k_{2}^{4} + 14 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(k_{1} + k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(\beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left({\left(3 \, k_{1}^{6} + 2 \, k_{1}^{5} k_{2} - 3 \, k_{1}^{4} k_{2}^{2} - 4 \, k_{1}^{3} k_{2}^{3} - 3 \, k_{1}^{2} k_{2}^{4} + 2 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left(2 \, {\left(k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(3 \, k_{1}^{6} + 10 \, k_{1}^{5} k_{2} + 13 \, k_{1}^{4} k_{2}^{2} + 12 \, k_{1}^{3} k_{2}^{3} + 13 \, k_{1}^{2} k_{2}^{4} + 10 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left({\left(k_{1}^{6} - 2 \, k_{1}^{5} k_{2} - k_{1}^{4} k_{2}^{2} + 4 \, k_{1}^{3} k_{2}^{3} - k_{1}^{2} k_{2}^{4} - 2 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left({\left(2 \, k_{1} + 3 \, k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(k_{1}^{6} + 2 \, k_{1}^{5} k_{2} - k_{1}^{4} k_{2}^{2} - 4 \, k_{1}^{3} k_{2}^{3} - k_{1}^{2} k_{2}^{4} + 2 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left({\left(k_{1} + 3 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(3 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(k_{1}^{6} + 6 \, k_{1}^{5} k_{2} + 15 \, k_{1}^{4} k_{2}^{2} + 20 \, k_{1}^{3} k_{2}^{3} + 15 \, k_{1}^{2} k_{2}^{4} + 6 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left(k_{1} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{6} + 6 \, k_{1}^{5} k_{2} + 15 \, k_{1}^{4} k_{2}^{2} + 20 \, k_{1}^{3} k_{2}^{3} + 15 \, k_{1}^{2} k_{2}^{4} + 6 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left(2 \, k_{1} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} D[0]\left(\alpha\right)\left(x, t_{1}, t_{2}, t_{3}\right)^{2} D[1]\left(\alpha\right)\left(x, t_{1}, t_{2}, t_{3}\right) + 2 \, {\left({\left({\left({\left(k_{1}^{6} + 2 \, k_{1}^{5} k_{2} - k_{1}^{4} k_{2}^{2} - 4 \, k_{1}^{3} k_{2}^{3} - k_{1}^{2} k_{2}^{4} + 2 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left({\left(3 \, k_{1} + k_{2}\right)} x + 3 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{6} + 6 \, k_{1}^{5} k_{2} + 15 \, k_{1}^{4} k_{2}^{2} + 20 \, k_{1}^{3} k_{2}^{3} + 15 \, k_{1}^{2} k_{2}^{4} + 6 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left(k_{2} x\right)} + {\left(3 \, k_{1}^{6} + 10 \, k_{1}^{5} k_{2} + 13 \, k_{1}^{4} k_{2}^{2} + 12 \, k_{1}^{3} k_{2}^{3} + 13 \, k_{1}^{2} k_{2}^{4} + 10 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(2 \, k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(3 \, k_{1}^{6} + 14 \, k_{1}^{5} k_{2} + 29 \, k_{1}^{4} k_{2}^{2} + 36 \, k_{1}^{3} k_{2}^{3} + 29 \, k_{1}^{2} k_{2}^{4} + 14 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(k_{1} + k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(\beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left({\left(k_{1}^{6} - 2 \, k_{1}^{5} k_{2} - k_{1}^{4} k_{2}^{2} + 4 \, k_{1}^{3} k_{2}^{3} - k_{1}^{2} k_{2}^{4} - 2 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left({\left(3 \, k_{1} + 2 \, k_{2}\right)} x + 3 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{6} + 6 \, k_{1}^{5} k_{2} + 15 \, k_{1}^{4} k_{2}^{2} + 20 \, k_{1}^{3} k_{2}^{3} + 15 \, k_{1}^{2} k_{2}^{4} + 6 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left(2 \, k_{2} x\right)} + {\left(3 \, k_{1}^{6} + 2 \, k_{1}^{5} k_{2} - 3 \, k_{1}^{4} k_{2}^{2} - 4 \, k_{1}^{3} k_{2}^{3} - 3 \, k_{1}^{2} k_{2}^{4} + 2 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left(2 \, {\left(k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(3 \, k_{1}^{6} + 10 \, k_{1}^{5} k_{2} + 13 \, k_{1}^{4} k_{2}^{2} + 12 \, k_{1}^{3} k_{2}^{3} + 13 \, k_{1}^{2} k_{2}^{4} + 10 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} D[1]\left(\beta\right)\left(x, t_{1}, t_{2}, t_{3}\right) - 4 \, {\left({\left({\left(k_{1}^{5} k_{2} + 4 \, k_{1}^{4} k_{2}^{2} + 6 \, k_{1}^{3} k_{2}^{3} + 4 \, k_{1}^{2} k_{2}^{4} + k_{1} k_{2}^{5}\right)} e^{\left({\left(2 \, k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{5} k_{2} + 4 \, k_{1}^{4} k_{2}^{2} + 6 \, k_{1}^{3} k_{2}^{3} + 4 \, k_{1}^{2} k_{2}^{4} + k_{1} k_{2}^{5}\right)} e^{\left({\left(k_{1} + k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(\beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left({\left(k_{1}^{5} k_{2} - 2 \, k_{1}^{3} k_{2}^{3} + k_{1} k_{2}^{5}\right)} e^{\left(2 \, {\left(k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{5} k_{2} + 4 \, k_{1}^{4} k_{2}^{2} + 6 \, k_{1}^{3} k_{2}^{3} + 4 \, k_{1}^{2} k_{2}^{4} + k_{1} k_{2}^{5}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} D[1]\left(\alpha\right)\left(x, t_{1}, t_{2}, t_{3}\right)\right)} D[0]\left(\beta\right)\left(x, t_{1}, t_{2}, t_{3}\right)^{2} + 2 \, {\left({\left({\left(3 \, k_{1}^{6} + 10 \, k_{1}^{5} k_{2} + 13 \, k_{1}^{4} k_{2}^{2} + 12 \, k_{1}^{3} k_{2}^{3} + 13 \, k_{1}^{2} k_{2}^{4} + 10 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(2 \, k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(3 \, k_{1}^{6} + 14 \, k_{1}^{5} k_{2} + 29 \, k_{1}^{4} k_{2}^{2} + 36 \, k_{1}^{3} k_{2}^{3} + 29 \, k_{1}^{2} k_{2}^{4} + 14 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(k_{1} + k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(\beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left({\left(3 \, k_{1}^{6} + 2 \, k_{1}^{5} k_{2} - 3 \, k_{1}^{4} k_{2}^{2} - 4 \, k_{1}^{3} k_{2}^{3} - 3 \, k_{1}^{2} k_{2}^{4} + 2 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left(2 \, {\left(k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(3 \, k_{1}^{6} + 10 \, k_{1}^{5} k_{2} + 13 \, k_{1}^{4} k_{2}^{2} + 12 \, k_{1}^{3} k_{2}^{3} + 13 \, k_{1}^{2} k_{2}^{4} + 10 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left({\left(k_{1}^{6} - 2 \, k_{1}^{5} k_{2} - k_{1}^{4} k_{2}^{2} + 4 \, k_{1}^{3} k_{2}^{3} - k_{1}^{2} k_{2}^{4} - 2 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left({\left(2 \, k_{1} + 3 \, k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{6} + 2 \, k_{1}^{5} k_{2} - k_{1}^{4} k_{2}^{2} - 4 \, k_{1}^{3} k_{2}^{3} - k_{1}^{2} k_{2}^{4} + 2 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left({\left(k_{1} + 3 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(3 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{6} + 6 \, k_{1}^{5} k_{2} + 15 \, k_{1}^{4} k_{2}^{2} + 20 \, k_{1}^{3} k_{2}^{3} + 15 \, k_{1}^{2} k_{2}^{4} + 6 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left(k_{1} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{6} + 6 \, k_{1}^{5} k_{2} + 15 \, k_{1}^{4} k_{2}^{2} + 20 \, k_{1}^{3} k_{2}^{3} + 15 \, k_{1}^{2} k_{2}^{4} + 6 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left(2 \, k_{1} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} D[0, 0]\left(\alpha\right)\left(x, t_{1}, t_{2}, t_{3}\right) D[1]\left(\alpha\right)\left(x, t_{1}, t_{2}, t_{3}\right) + 4 \, {\left({\left({\left({\left(3 \, k_{1}^{6} + 10 \, k_{1}^{5} k_{2} + 13 \, k_{1}^{4} k_{2}^{2} + 12 \, k_{1}^{3} k_{2}^{3} + 13 \, k_{1}^{2} k_{2}^{4} + 10 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(2 \, k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(3 \, k_{1}^{6} + 14 \, k_{1}^{5} k_{2} + 29 \, k_{1}^{4} k_{2}^{2} + 36 \, k_{1}^{3} k_{2}^{3} + 29 \, k_{1}^{2} k_{2}^{4} + 14 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(k_{1} + k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(\beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left({\left(3 \, k_{1}^{6} + 2 \, k_{1}^{5} k_{2} - 3 \, k_{1}^{4} k_{2}^{2} - 4 \, k_{1}^{3} k_{2}^{3} - 3 \, k_{1}^{2} k_{2}^{4} + 2 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left(2 \, {\left(k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(3 \, k_{1}^{6} + 10 \, k_{1}^{5} k_{2} + 13 \, k_{1}^{4} k_{2}^{2} + 12 \, k_{1}^{3} k_{2}^{3} + 13 \, k_{1}^{2} k_{2}^{4} + 10 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left({\left(k_{1}^{6} - 2 \, k_{1}^{5} k_{2} - k_{1}^{4} k_{2}^{2} + 4 \, k_{1}^{3} k_{2}^{3} - k_{1}^{2} k_{2}^{4} - 2 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left({\left(2 \, k_{1} + 3 \, k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{6} + 2 \, k_{1}^{5} k_{2} - k_{1}^{4} k_{2}^{2} - 4 \, k_{1}^{3} k_{2}^{3} - k_{1}^{2} k_{2}^{4} + 2 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left({\left(k_{1} + 3 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(3 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{6} + 6 \, k_{1}^{5} k_{2} + 15 \, k_{1}^{4} k_{2}^{2} + 20 \, k_{1}^{3} k_{2}^{3} + 15 \, k_{1}^{2} k_{2}^{4} + 6 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left(k_{1} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{6} + 6 \, k_{1}^{5} k_{2} + 15 \, k_{1}^{4} k_{2}^{2} + 20 \, k_{1}^{3} k_{2}^{3} + 15 \, k_{1}^{2} k_{2}^{4} + 6 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left(2 \, k_{1} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} D[0, 1]\left(\alpha\right)\left(x, t_{1}, t_{2}, t_{3}\right) - {\left({\left({\left(3 \, k_{1}^{7} + 10 \, k_{1}^{6} k_{2} + 9 \, k_{1}^{5} k_{2}^{2} - 4 \, k_{1}^{4} k_{2}^{3} - 11 \, k_{1}^{3} k_{2}^{4} - 6 \, k_{1}^{2} k_{2}^{5} - k_{1} k_{2}^{6}\right)} e^{\left({\left(2 \, k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(3 \, k_{1}^{7} + 14 \, k_{1}^{6} k_{2} + 25 \, k_{1}^{5} k_{2}^{2} + 20 \, k_{1}^{4} k_{2}^{3} + 5 \, k_{1}^{3} k_{2}^{4} - 2 \, k_{1}^{2} k_{2}^{5} - k_{1} k_{2}^{6}\right)} e^{\left({\left(k_{1} + k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(\beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left({\left(3 \, k_{1}^{7} + 2 \, k_{1}^{6} k_{2} - 7 \, k_{1}^{5} k_{2}^{2} - 4 \, k_{1}^{4} k_{2}^{3} + 5 \, k_{1}^{3} k_{2}^{4} + 2 \, k_{1}^{2} k_{2}^{5} - k_{1} k_{2}^{6}\right)} e^{\left(2 \, {\left(k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(3 \, k_{1}^{7} + 10 \, k_{1}^{6} k_{2} + 9 \, k_{1}^{5} k_{2}^{2} - 4 \, k_{1}^{4} k_{2}^{3} - 11 \, k_{1}^{3} k_{2}^{4} - 6 \, k_{1}^{2} k_{2}^{5} - k_{1} k_{2}^{6}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left({\left(k_{1}^{7} - 2 \, k_{1}^{6} k_{2} - k_{1}^{5} k_{2}^{2} + 4 \, k_{1}^{4} k_{2}^{3} - k_{1}^{3} k_{2}^{4} - 2 \, k_{1}^{2} k_{2}^{5} + k_{1} k_{2}^{6}\right)} e^{\left({\left(2 \, k_{1} + 3 \, k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(k_{1}^{7} + 2 \, k_{1}^{6} k_{2} - k_{1}^{5} k_{2}^{2} - 4 \, k_{1}^{4} k_{2}^{3} - k_{1}^{3} k_{2}^{4} + 2 \, k_{1}^{2} k_{2}^{5} + k_{1} k_{2}^{6}\right)} e^{\left({\left(k_{1} + 3 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(3 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(k_{1}^{7} + 6 \, k_{1}^{6} k_{2} + 15 \, k_{1}^{5} k_{2}^{2} + 20 \, k_{1}^{4} k_{2}^{3} + 15 \, k_{1}^{3} k_{2}^{4} + 6 \, k_{1}^{2} k_{2}^{5} + k_{1} k_{2}^{6}\right)} e^{\left(k_{1} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{7} + 6 \, k_{1}^{6} k_{2} + 15 \, k_{1}^{5} k_{2}^{2} + 20 \, k_{1}^{4} k_{2}^{3} + 15 \, k_{1}^{3} k_{2}^{4} + 6 \, k_{1}^{2} k_{2}^{5} + k_{1} k_{2}^{6}\right)} e^{\left(2 \, k_{1} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} D[1]\left(\alpha\right)\left(x, t_{1}, t_{2}, t_{3}\right)\right)} D[0]\left(\alpha\right)\left(x, t_{1}, t_{2}, t_{3}\right) + 2 \, {\left({\left({\left({\left(k_{1}^{6} + 2 \, k_{1}^{5} k_{2} - k_{1}^{4} k_{2}^{2} - 4 \, k_{1}^{3} k_{2}^{3} - k_{1}^{2} k_{2}^{4} + 2 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left({\left(3 \, k_{1} + k_{2}\right)} x + 3 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{6} + 6 \, k_{1}^{5} k_{2} + 15 \, k_{1}^{4} k_{2}^{2} + 20 \, k_{1}^{3} k_{2}^{3} + 15 \, k_{1}^{2} k_{2}^{4} + 6 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left(k_{2} x\right)} + {\left(3 \, k_{1}^{6} + 10 \, k_{1}^{5} k_{2} + 13 \, k_{1}^{4} k_{2}^{2} + 12 \, k_{1}^{3} k_{2}^{3} + 13 \, k_{1}^{2} k_{2}^{4} + 10 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(2 \, k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(3 \, k_{1}^{6} + 14 \, k_{1}^{5} k_{2} + 29 \, k_{1}^{4} k_{2}^{2} + 36 \, k_{1}^{3} k_{2}^{3} + 29 \, k_{1}^{2} k_{2}^{4} + 14 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(k_{1} + k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(\beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left({\left(k_{1}^{6} - 2 \, k_{1}^{5} k_{2} - k_{1}^{4} k_{2}^{2} + 4 \, k_{1}^{3} k_{2}^{3} - k_{1}^{2} k_{2}^{4} - 2 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left({\left(3 \, k_{1} + 2 \, k_{2}\right)} x + 3 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{6} + 6 \, k_{1}^{5} k_{2} + 15 \, k_{1}^{4} k_{2}^{2} + 20 \, k_{1}^{3} k_{2}^{3} + 15 \, k_{1}^{2} k_{2}^{4} + 6 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left(2 \, k_{2} x\right)} + {\left(3 \, k_{1}^{6} + 2 \, k_{1}^{5} k_{2} - 3 \, k_{1}^{4} k_{2}^{2} - 4 \, k_{1}^{3} k_{2}^{3} - 3 \, k_{1}^{2} k_{2}^{4} + 2 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left(2 \, {\left(k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(3 \, k_{1}^{6} + 10 \, k_{1}^{5} k_{2} + 13 \, k_{1}^{4} k_{2}^{2} + 12 \, k_{1}^{3} k_{2}^{3} + 13 \, k_{1}^{2} k_{2}^{4} + 10 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} D[1]\left(\beta\right)\left(x, t_{1}, t_{2}, t_{3}\right) - 4 \, {\left({\left({\left(k_{1}^{5} k_{2} + 4 \, k_{1}^{4} k_{2}^{2} + 6 \, k_{1}^{3} k_{2}^{3} + 4 \, k_{1}^{2} k_{2}^{4} + k_{1} k_{2}^{5}\right)} e^{\left({\left(2 \, k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{5} k_{2} + 4 \, k_{1}^{4} k_{2}^{2} + 6 \, k

...

_{1}^{2} k_{2}^{4} + 6 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left(2 \, k_{2} x\right)} + {\left(3 \, k_{1}^{6} + 2 \, k_{1}^{5} k_{2} - 3 \, k_{1}^{4} k_{2}^{2} - 4 \, k_{1}^{3} k_{2}^{3} - 3 \, k_{1}^{2} k_{2}^{4} + 2 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left(2 \, {\left(k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(3 \, k_{1}^{6} + 10 \, k_{1}^{5} k_{2} + 13 \, k_{1}^{4} k_{2}^{2} + 12 \, k_{1}^{3} k_{2}^{3} + 13 \, k_{1}^{2} k_{2}^{4} + 10 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} D[0, 1]\left(\beta\right)\left(x, t_{1}, t_{2}, t_{3}\right) - 4 \, {\left({\left({\left(k_{1}^{5} k_{2} + 4 \, k_{1}^{4} k_{2}^{2} + 6 \, k_{1}^{3} k_{2}^{3} + 4 \, k_{1}^{2} k_{2}^{4} + k_{1} k_{2}^{5}\right)} e^{\left({\left(2 \, k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{5} k_{2} + 4 \, k_{1}^{4} k_{2}^{2} + 6 \, k_{1}^{3} k_{2}^{3} + 4 \, k_{1}^{2} k_{2}^{4} + k_{1} k_{2}^{5}\right)} e^{\left({\left(k_{1} + k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(\beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left({\left(k_{1}^{5} k_{2} - 2 \, k_{1}^{3} k_{2}^{3} + k_{1} k_{2}^{5}\right)} e^{\left(2 \, {\left(k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{5} k_{2} + 4 \, k_{1}^{4} k_{2}^{2} + 6 \, k_{1}^{3} k_{2}^{3} + 4 \, k_{1}^{2} k_{2}^{4} + k_{1} k_{2}^{5}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} D[0, 1]\left(\alpha\right)\left(x, t_{1}, t_{2}, t_{3}\right) + 4 \, {\left({\left({\left(k_{1}^{6} k_{2} + 3 \, k_{1}^{5} k_{2}^{2} + 2 \, k_{1}^{4} k_{2}^{3} - 2 \, k_{1}^{3} k_{2}^{4} - 3 \, k_{1}^{2} k_{2}^{5} - k_{1} k_{2}^{6}\right)} e^{\left({\left(2 \, k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(k_{1}^{6} k_{2} + 5 \, k_{1}^{5} k_{2}^{2} + 10 \, k_{1}^{4} k_{2}^{3} + 10 \, k_{1}^{3} k_{2}^{4} + 5 \, k_{1}^{2} k_{2}^{5} + k_{1} k_{2}^{6}\right)} e^{\left({\left(k_{1} + k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(\beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left({\left(k_{1}^{6} k_{2} + k_{1}^{5} k_{2}^{2} - 2 \, k_{1}^{4} k_{2}^{3} - 2 \, k_{1}^{3} k_{2}^{4} + k_{1}^{2} k_{2}^{5} + k_{1} k_{2}^{6}\right)} e^{\left(2 \, {\left(k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(k_{1}^{6} k_{2} + 3 \, k_{1}^{5} k_{2}^{2} + 2 \, k_{1}^{4} k_{2}^{3} - 2 \, k_{1}^{3} k_{2}^{4} - 3 \, k_{1}^{2} k_{2}^{5} - k_{1} k_{2}^{6}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} D[1]\left(\alpha\right)\left(x, t_{1}, t_{2}, t_{3}\right) - {\left(4 \, {\left({\left({\left(k_{1}^{5} k_{2} + 4 \, k_{1}^{4} k_{2}^{2} + 6 \, k_{1}^{3} k_{2}^{3} + 4 \, k_{1}^{2} k_{2}^{4} + k_{1} k_{2}^{5}\right)} e^{\left({\left(2 \, k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{5} k_{2} + 4 \, k_{1}^{4} k_{2}^{2} + 6 \, k_{1}^{3} k_{2}^{3} + 4 \, k_{1}^{2} k_{2}^{4} + k_{1} k_{2}^{5}\right)} e^{\left({\left(k_{1} + k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(\beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left({\left(k_{1}^{5} k_{2} - 2 \, k_{1}^{3} k_{2}^{3} + k_{1} k_{2}^{5}\right)} e^{\left(2 \, {\left(k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{5} k_{2} + 4 \, k_{1}^{4} k_{2}^{2} + 6 \, k_{1}^{3} k_{2}^{3} + 4 \, k_{1}^{2} k_{2}^{4} + k_{1} k_{2}^{5}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} D[0]\left(\alpha\right)\left(x, t_{1}, t_{2}, t_{3}\right) + {\left({\left(k_{1}^{6} k_{2} + 2 \, k_{1}^{5} k_{2}^{2} - 5 \, k_{1}^{4} k_{2}^{3} - 20 \, k_{1}^{3} k_{2}^{4} - 25 \, k_{1}^{2} k_{2}^{5} - 14 \, k_{1} k_{2}^{6} - 3 \, k_{2}^{7}\right)} e^{\left({\left(k_{1} + k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(k_{1}^{6} k_{2} + 2 \, k_{1}^{5} k_{2}^{2} - k_{1}^{4} k_{2}^{3} - 4 \, k_{1}^{3} k_{2}^{4} - k_{1}^{2} k_{2}^{5} + 2 \, k_{1} k_{2}^{6} + k_{2}^{7}\right)} e^{\left({\left(3 \, k_{1} + k_{2}\right)} x + 3 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{6} k_{2} + 6 \, k_{1}^{5} k_{2}^{2} + 11 \, k_{1}^{4} k_{2}^{3} + 4 \, k_{1}^{3} k_{2}^{4} - 9 \, k_{1}^{2} k_{2}^{5} - 10 \, k_{1} k_{2}^{6} - 3 \, k_{2}^{7}\right)} e^{\left({\left(2 \, k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(k_{1}^{6} k_{2} + 6 \, k_{1}^{5} k_{2}^{2} + 15 \, k_{1}^{4} k_{2}^{3} + 20 \, k_{1}^{3} k_{2}^{4} + 15 \, k_{1}^{2} k_{2}^{5} + 6 \, k_{1} k_{2}^{6} + k_{2}^{7}\right)} e^{\left(k_{2} x\right)}\right)} e^{\left(\beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left({\left(k_{1}^{6} k_{2} - 2 \, k_{1}^{5} k_{2}^{2} - 5 \, k_{1}^{4} k_{2}^{3} + 4 \, k_{1}^{3} k_{2}^{4} + 7 \, k_{1}^{2} k_{2}^{5} - 2 \, k_{1} k_{2}^{6} - 3 \, k_{2}^{7}\right)} e^{\left(2 \, {\left(k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(k_{1}^{6} k_{2} - 2 \, k_{1}^{5} k_{2}^{2} - k_{1}^{4} k_{2}^{3} + 4 \, k_{1}^{3} k_{2}^{4} - k_{1}^{2} k_{2}^{5} - 2 \, k_{1} k_{2}^{6} + k_{2}^{7}\right)} e^{\left({\left(3 \, k_{1} + 2 \, k_{2}\right)} x + 3 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{6} k_{2} + 6 \, k_{1}^{5} k_{2}^{2} + 11 \, k_{1}^{4} k_{2}^{3} + 4 \, k_{1}^{3} k_{2}^{4} - 9 \, k_{1}^{2} k_{2}^{5} - 10 \, k_{1} k_{2}^{6} - 3 \, k_{2}^{7}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(k_{1}^{6} k_{2} + 6 \, k_{1}^{5} k_{2}^{2} + 15 \, k_{1}^{4} k_{2}^{3} + 20 \, k_{1}^{3} k_{2}^{4} + 15 \, k_{1}^{2} k_{2}^{5} + 6 \, k_{1} k_{2}^{6} + k_{2}^{7}\right)} e^{\left(2 \, k_{2} x\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} D[1]\left(\beta\right)\left(x, t_{1}, t_{2}, t_{3}\right)\right)} D[0]\left(\beta\right)\left(x, t_{1}, t_{2}, t_{3}\right) + 2 \, {\left(4 \, {\left({\left({\left(k_{1}^{5} k_{2} + 4 \, k_{1}^{4} k_{2}^{2} + 6 \, k_{1}^{3} k_{2}^{3} + 4 \, k_{1}^{2} k_{2}^{4} + k_{1} k_{2}^{5}\right)} e^{\left({\left(2 \, k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(k_{1}^{5} k_{2} + 4 \, k_{1}^{4} k_{2}^{2} + 6 \, k_{1}^{3} k_{2}^{3} + 4 \, k_{1}^{2} k_{2}^{4} + k_{1} k_{2}^{5}\right)} e^{\left({\left(k_{1} + k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(\beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left({\left(k_{1}^{5} k_{2} - 2 \, k_{1}^{3} k_{2}^{3} + k_{1} k_{2}^{5}\right)} e^{\left(2 \, {\left(k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(k_{1}^{5} k_{2} + 4 \, k_{1}^{4} k_{2}^{2} + 6 \, k_{1}^{3} k_{2}^{3} + 4 \, k_{1}^{2} k_{2}^{4} + k_{1} k_{2}^{5}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} D[0]\left(\alpha\right)\left(x, t_{1}, t_{2}, t_{3}\right)^{2} - 4 \, {\left({\left({\left(k_{1}^{5} k_{2} + 4 \, k_{1}^{4} k_{2}^{2} + 6 \, k_{1}^{3} k_{2}^{3} + 4 \, k_{1}^{2} k_{2}^{4} + k_{1} k_{2}^{5}\right)} e^{\left({\left(2 \, k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{5} k_{2} + 4 \, k_{1}^{4} k_{2}^{2} + 6 \, k_{1}^{3} k_{2}^{3} + 4 \, k_{1}^{2} k_{2}^{4} + k_{1} k_{2}^{5}\right)} e^{\left({\left(k_{1} + k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(\beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left({\left(k_{1}^{5} k_{2} - 2 \, k_{1}^{3} k_{2}^{3} + k_{1} k_{2}^{5}\right)} e^{\left(2 \, {\left(k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{5} k_{2} + 4 \, k_{1}^{4} k_{2}^{2} + 6 \, k_{1}^{3} k_{2}^{3} + 4 \, k_{1}^{2} k_{2}^{4} + k_{1} k_{2}^{5}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} D[0, 0]\left(\alpha\right)\left(x, t_{1}, t_{2}, t_{3}\right) + 8 \, {\left({\left({\left(k_{1}^{6} k_{2} + 3 \, k_{1}^{5} k_{2}^{2} + 2 \, k_{1}^{4} k_{2}^{3} - 2 \, k_{1}^{3} k_{2}^{4} - 3 \, k_{1}^{2} k_{2}^{5} - k_{1} k_{2}^{6}\right)} e^{\left({\left(2 \, k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(k_{1}^{6} k_{2} + 5 \, k_{1}^{5} k_{2}^{2} + 10 \, k_{1}^{4} k_{2}^{3} + 10 \, k_{1}^{3} k_{2}^{4} + 5 \, k_{1}^{2} k_{2}^{5} + k_{1} k_{2}^{6}\right)} e^{\left({\left(k_{1} + k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(\beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left({\left(k_{1}^{6} k_{2} + k_{1}^{5} k_{2}^{2} - 2 \, k_{1}^{4} k_{2}^{3} - 2 \, k_{1}^{3} k_{2}^{4} + k_{1}^{2} k_{2}^{5} + k_{1} k_{2}^{6}\right)} e^{\left(2 \, {\left(k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(k_{1}^{6} k_{2} + 3 \, k_{1}^{5} k_{2}^{2} + 2 \, k_{1}^{4} k_{2}^{3} - 2 \, k_{1}^{3} k_{2}^{4} - 3 \, k_{1}^{2} k_{2}^{5} - k_{1} k_{2}^{6}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} D[0]\left(\alpha\right)\left(x, t_{1}, t_{2}, t_{3}\right) + {\left({\left(k_{1}^{6} k_{2}^{2} + 2 \, k_{1}^{5} k_{2}^{3} - k_{1}^{4} k_{2}^{4} - 4 \, k_{1}^{3} k_{2}^{5} - k_{1}^{2} k_{2}^{6} + 2 \, k_{1} k_{2}^{7} + k_{2}^{8}\right)} e^{\left({\left(3 \, k_{1} + k_{2}\right)} x + 3 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{6} k_{2}^{2} + 6 \, k_{1}^{5} k_{2}^{3} + 15 \, k_{1}^{4} k_{2}^{4} + 20 \, k_{1}^{3} k_{2}^{5} + 15 \, k_{1}^{2} k_{2}^{6} + 6 \, k_{1} k_{2}^{7} + k_{2}^{8}\right)} e^{\left(k_{2} x\right)} - {\left(4 \, k_{1}^{7} k_{2} + 21 \, k_{1}^{6} k_{2}^{2} + 42 \, k_{1}^{5} k_{2}^{3} + 35 \, k_{1}^{4} k_{2}^{4} - 21 \, k_{1}^{2} k_{2}^{6} - 14 \, k_{1} k_{2}^{7} - 3 \, k_{2}^{8}\right)} e^{\left({\left(k_{1} + k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(4 \, k_{1}^{7} k_{2} + 11 \, k_{1}^{6} k_{2}^{2} + 2 \, k_{1}^{5} k_{2}^{3} - 19 \, k_{1}^{4} k_{2}^{4} - 16 \, k_{1}^{3} k_{2}^{5} + 5 \, k_{1}^{2} k_{2}^{6} + 10 \, k_{1} k_{2}^{7} + 3 \, k_{2}^{8}\right)} e^{\left({\left(2 \, k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(\beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left({\left(k_{1}^{6} k_{2}^{2} - 2 \, k_{1}^{5} k_{2}^{3} - k_{1}^{4} k_{2}^{4} + 4 \, k_{1}^{3} k_{2}^{5} - k_{1}^{2} k_{2}^{6} - 2 \, k_{1} k_{2}^{7} + k_{2}^{8}\right)} e^{\left({\left(3 \, k_{1} + 2 \, k_{2}\right)} x + 3 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{6} k_{2}^{2} + 6 \, k_{1}^{5} k_{2}^{3} + 15 \, k_{1}^{4} k_{2}^{4} + 20 \, k_{1}^{3} k_{2}^{5} + 15 \, k_{1}^{2} k_{2}^{6} + 6 \, k_{1} k_{2}^{7} + k_{2}^{8}\right)} e^{\left(2 \, k_{2} x\right)} - {\left(4 \, k_{1}^{7} k_{2} + 5 \, k_{1}^{6} k_{2}^{2} - 10 \, k_{1}^{5} k_{2}^{3} - 13 \, k_{1}^{4} k_{2}^{4} + 8 \, k_{1}^{3} k_{2}^{5} + 11 \, k_{1}^{2} k_{2}^{6} - 2 \, k_{1} k_{2}^{7} - 3 \, k_{2}^{8}\right)} e^{\left(2 \, {\left(k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(4 \, k_{1}^{7} k_{2} + 11 \, k_{1}^{6} k_{2}^{2} + 2 \, k_{1}^{5} k_{2}^{3} - 19 \, k_{1}^{4} k_{2}^{4} - 16 \, k_{1}^{3} k_{2}^{5} + 5 \, k_{1}^{2} k_{2}^{6} + 10 \, k_{1} k_{2}^{7} + 3 \, k_{2}^{8}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} D[1]\left(\beta\right)\left(x, t_{1}, t_{2}, t_{3}\right) + 2 \, {\left({\left(3 \, {\left(k_{1}^{6} + 2 \, k_{1}^{5} k_{2} - k_{1}^{4} k_{2}^{2} - 4 \, k_{1}^{3} k_{2}^{3} - k_{1}^{2} k_{2}^{4} + 2 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left({\left(3 \, k_{1} + k_{2}\right)} x + 3 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + 2 \, {\left(3 \, k_{1}^{6} + 10 \, k_{1}^{5} k_{2} + 13 \, k_{1}^{4} k_{2}^{2} + 12 \, k_{1}^{3} k_{2}^{3} + 13 \, k_{1}^{2} k_{2}^{4} + 10 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(2 \, k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(3 \, k_{1}^{6} + 14 \, k_{1}^{5} k_{2} + 29 \, k_{1}^{4} k_{2}^{2} + 36 \, k_{1}^{3} k_{2}^{3} + 29 \, k_{1}^{2} k_{2}^{4} + 14 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(k_{1} + k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(\beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(3 \, {\left(k_{1}^{6} - 2 \, k_{1}^{5} k_{2} - k_{1}^{4} k_{2}^{2} + 4 \, k_{1}^{3} k_{2}^{3} - k_{1}^{2} k_{2}^{4} - 2 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left({\left(3 \, k_{1} + 2 \, k_{2}\right)} x + 3 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + 2 \, {\left(3 \, k_{1}^{6} + 2 \, k_{1}^{5} k_{2} - 3 \, k_{1}^{4} k_{2}^{2} - 4 \, k_{1}^{3} k_{2}^{3} - 3 \, k_{1}^{2} k_{2}^{4} + 2 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left(2 \, {\left(k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(3 \, k_{1}^{6} + 10 \, k_{1}^{5} k_{2} + 13 \, k_{1}^{4} k_{2}^{2} + 12 \, k_{1}^{3} k_{2}^{3} + 13 \, k_{1}^{2} k_{2}^{4} + 10 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left({\left(k_{1}^{6} - 6 \, k_{1}^{5} k_{2} + 15 \, k_{1}^{4} k_{2}^{2} - 20 \, k_{1}^{3} k_{2}^{3} + 15 \, k_{1}^{2} k_{2}^{4} - 6 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left(3 \, {\left(k_{1} + k_{2}\right)} x + 3 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + 2 \, {\left(k_{1}^{6} - 2 \, k_{1}^{5} k_{2} - k_{1}^{4} k_{2}^{2} + 4 \, k_{1}^{3} k_{2}^{3} - k_{1}^{2} k_{2}^{4} - 2 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left({\left(2 \, k_{1} + 3 \, k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{6} + 2 \, k_{1}^{5} k_{2} - k_{1}^{4} k_{2}^{2} - 4 \, k_{1}^{3} k_{2}^{3} - k_{1}^{2} k_{2}^{4} + 2 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left({\left(k_{1} + 3 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(3 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{6} + 6 \, k_{1}^{5} k_{2} + 15 \, k_{1}^{4} k_{2}^{2} + 20 \, k_{1}^{3} k_{2}^{3} + 15 \, k_{1}^{2} k_{2}^{4} + 6 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left(k_{1} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + 2 \, {\left(k_{1}^{6} + 6 \, k_{1}^{5} k_{2} + 15 \, k_{1}^{4} k_{2}^{2} + 20 \, k_{1}^{3} k_{2}^{3} + 15 \, k_{1}^{2} k_{2}^{4} + 6 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left(2 \, k_{1} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{6} + 6 \, k_{1}^{5} k_{2} + 15 \, k_{1}^{4} k_{2}^{2} + 20 \, k_{1}^{3} k_{2}^{3} + 15 \, k_{1}^{2} k_{2}^{4} + 6 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left(3 \, k_{1} x + 3 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} D[0, 0, 1]\left(\alpha\right)\left(x, t_{1}, t_{2}, t_{3}\right)

WARNING: Output truncated!  
full_output.txt



\newcommand{\Bold}[1]{\mathbf{#1}}-2 \, {\left({\left({\left(3 \, k_{1}^{6} + 10 \, k_{1}^{5} k_{2} + 13 \, k_{1}^{4} k_{2}^{2} + 12 \, k_{1}^{3} k_{2}^{3} + 13 \, k_{1}^{2} k_{2}^{4} + 10 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(2 \, k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(3 \, k_{1}^{6} + 14 \, k_{1}^{5} k_{2} + 29 \, k_{1}^{4} k_{2}^{2} + 36 \, k_{1}^{3} k_{2}^{3} + 29 \, k_{1}^{2} k_{2}^{4} + 14 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(k_{1} + k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(\beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left({\left(3 \, k_{1}^{6} + 2 \, k_{1}^{5} k_{2} - 3 \, k_{1}^{4} k_{2}^{2} - 4 \, k_{1}^{3} k_{2}^{3} - 3 \, k_{1}^{2} k_{2}^{4} + 2 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left(2 \, {\left(k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(3 \, k_{1}^{6} + 10 \, k_{1}^{5} k_{2} + 13 \, k_{1}^{4} k_{2}^{2} + 12 \, k_{1}^{3} k_{2}^{3} + 13 \, k_{1}^{2} k_{2}^{4} + 10 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left({\left(k_{1}^{6} - 2 \, k_{1}^{5} k_{2} - k_{1}^{4} k_{2}^{2} + 4 \, k_{1}^{3} k_{2}^{3} - k_{1}^{2} k_{2}^{4} - 2 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left({\left(2 \, k_{1} + 3 \, k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(k_{1}^{6} + 2 \, k_{1}^{5} k_{2} - k_{1}^{4} k_{2}^{2} - 4 \, k_{1}^{3} k_{2}^{3} - k_{1}^{2} k_{2}^{4} + 2 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left({\left(k_{1} + 3 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(3 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(k_{1}^{6} + 6 \, k_{1}^{5} k_{2} + 15 \, k_{1}^{4} k_{2}^{2} + 20 \, k_{1}^{3} k_{2}^{3} + 15 \, k_{1}^{2} k_{2}^{4} + 6 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left(k_{1} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{6} + 6 \, k_{1}^{5} k_{2} + 15 \, k_{1}^{4} k_{2}^{2} + 20 \, k_{1}^{3} k_{2}^{3} + 15 \, k_{1}^{2} k_{2}^{4} + 6 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left(2 \, k_{1} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} D[0]\left(\alpha\right)\left(x, t_{1}, t_{2}, t_{3}\right)^{2} D[1]\left(\alpha\right)\left(x, t_{1}, t_{2}, t_{3}\right) + 2 \, {\left({\left({\left({\left(k_{1}^{6} + 2 \, k_{1}^{5} k_{2} - k_{1}^{4} k_{2}^{2} - 4 \, k_{1}^{3} k_{2}^{3} - k_{1}^{2} k_{2}^{4} + 2 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left({\left(3 \, k_{1} + k_{2}\right)} x + 3 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{6} + 6 \, k_{1}^{5} k_{2} + 15 \, k_{1}^{4} k_{2}^{2} + 20 \, k_{1}^{3} k_{2}^{3} + 15 \, k_{1}^{2} k_{2}^{4} + 6 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left(k_{2} x\right)} + {\left(3 \, k_{1}^{6} + 10 \, k_{1}^{5} k_{2} + 13 \, k_{1}^{4} k_{2}^{2} + 12 \, k_{1}^{3} k_{2}^{3} + 13 \, k_{1}^{2} k_{2}^{4} + 10 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(2 \, k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(3 \, k_{1}^{6} + 14 \, k_{1}^{5} k_{2} + 29 \, k_{1}^{4} k_{2}^{2} + 36 \, k_{1}^{3} k_{2}^{3} + 29 \, k_{1}^{2} k_{2}^{4} + 14 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(k_{1} + k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(\beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left({\left(k_{1}^{6} - 2 \, k_{1}^{5} k_{2} - k_{1}^{4} k_{2}^{2} + 4 \, k_{1}^{3} k_{2}^{3} - k_{1}^{2} k_{2}^{4} - 2 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left({\left(3 \, k_{1} + 2 \, k_{2}\right)} x + 3 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{6} + 6 \, k_{1}^{5} k_{2} + 15 \, k_{1}^{4} k_{2}^{2} + 20 \, k_{1}^{3} k_{2}^{3} + 15 \, k_{1}^{2} k_{2}^{4} + 6 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left(2 \, k_{2} x\right)} + {\left(3 \, k_{1}^{6} + 2 \, k_{1}^{5} k_{2} - 3 \, k_{1}^{4} k_{2}^{2} - 4 \, k_{1}^{3} k_{2}^{3} - 3 \, k_{1}^{2} k_{2}^{4} + 2 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left(2 \, {\left(k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(3 \, k_{1}^{6} + 10 \, k_{1}^{5} k_{2} + 13 \, k_{1}^{4} k_{2}^{2} + 12 \, k_{1}^{3} k_{2}^{3} + 13 \, k_{1}^{2} k_{2}^{4} + 10 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} D[1]\left(\beta\right)\left(x, t_{1}, t_{2}, t_{3}\right) - 4 \, {\left({\left({\left(k_{1}^{5} k_{2} + 4 \, k_{1}^{4} k_{2}^{2} + 6 \, k_{1}^{3} k_{2}^{3} + 4 \, k_{1}^{2} k_{2}^{4} + k_{1} k_{2}^{5}\right)} e^{\left({\left(2 \, k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{5} k_{2} + 4 \, k_{1}^{4} k_{2}^{2} + 6 \, k_{1}^{3} k_{2}^{3} + 4 \, k_{1}^{2} k_{2}^{4} + k_{1} k_{2}^{5}\right)} e^{\left({\left(k_{1} + k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(\beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left({\left(k_{1}^{5} k_{2} - 2 \, k_{1}^{3} k_{2}^{3} + k_{1} k_{2}^{5}\right)} e^{\left(2 \, {\left(k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{5} k_{2} + 4 \, k_{1}^{4} k_{2}^{2} + 6 \, k_{1}^{3} k_{2}^{3} + 4 \, k_{1}^{2} k_{2}^{4} + k_{1} k_{2}^{5}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} D[1]\left(\alpha\right)\left(x, t_{1}, t_{2}, t_{3}\right)\right)} D[0]\left(\beta\right)\left(x, t_{1}, t_{2}, t_{3}\right)^{2} + 2 \, {\left({\left({\left(3 \, k_{1}^{6} + 10 \, k_{1}^{5} k_{2} + 13 \, k_{1}^{4} k_{2}^{2} + 12 \, k_{1}^{3} k_{2}^{3} + 13 \, k_{1}^{2} k_{2}^{4} + 10 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(2 \, k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(3 \, k_{1}^{6} + 14 \, k_{1}^{5} k_{2} + 29 \, k_{1}^{4} k_{2}^{2} + 36 \, k_{1}^{3} k_{2}^{3} + 29 \, k_{1}^{2} k_{2}^{4} + 14 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(k_{1} + k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(\beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left({\left(3 \, k_{1}^{6} + 2 \, k_{1}^{5} k_{2} - 3 \, k_{1}^{4} k_{2}^{2} - 4 \, k_{1}^{3} k_{2}^{3} - 3 \, k_{1}^{2} k_{2}^{4} + 2 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left(2 \, {\left(k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(3 \, k_{1}^{6} + 10 \, k_{1}^{5} k_{2} + 13 \, k_{1}^{4} k_{2}^{2} + 12 \, k_{1}^{3} k_{2}^{3} + 13 \, k_{1}^{2} k_{2}^{4} + 10 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left({\left(k_{1}^{6} - 2 \, k_{1}^{5} k_{2} - k_{1}^{4} k_{2}^{2} + 4 \, k_{1}^{3} k_{2}^{3} - k_{1}^{2} k_{2}^{4} - 2 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left({\left(2 \, k_{1} + 3 \, k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{6} + 2 \, k_{1}^{5} k_{2} - k_{1}^{4} k_{2}^{2} - 4 \, k_{1}^{3} k_{2}^{3} - k_{1}^{2} k_{2}^{4} + 2 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left({\left(k_{1} + 3 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(3 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{6} + 6 \, k_{1}^{5} k_{2} + 15 \, k_{1}^{4} k_{2}^{2} + 20 \, k_{1}^{3} k_{2}^{3} + 15 \, k_{1}^{2} k_{2}^{4} + 6 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left(k_{1} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{6} + 6 \, k_{1}^{5} k_{2} + 15 \, k_{1}^{4} k_{2}^{2} + 20 \, k_{1}^{3} k_{2}^{3} + 15 \, k_{1}^{2} k_{2}^{4} + 6 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left(2 \, k_{1} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} D[0, 0]\left(\alpha\right)\left(x, t_{1}, t_{2}, t_{3}\right) D[1]\left(\alpha\right)\left(x, t_{1}, t_{2}, t_{3}\right) + 4 \, {\left({\left({\left({\left(3 \, k_{1}^{6} + 10 \, k_{1}^{5} k_{2} + 13 \, k_{1}^{4} k_{2}^{2} + 12 \, k_{1}^{3} k_{2}^{3} + 13 \, k_{1}^{2} k_{2}^{4} + 10 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(2 \, k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(3 \, k_{1}^{6} + 14 \, k_{1}^{5} k_{2} + 29 \, k_{1}^{4} k_{2}^{2} + 36 \, k_{1}^{3} k_{2}^{3} + 29 \, k_{1}^{2} k_{2}^{4} + 14 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(k_{1} + k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(\beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left({\left(3 \, k_{1}^{6} + 2 \, k_{1}^{5} k_{2} - 3 \, k_{1}^{4} k_{2}^{2} - 4 \, k_{1}^{3} k_{2}^{3} - 3 \, k_{1}^{2} k_{2}^{4} + 2 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left(2 \, {\left(k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(3 \, k_{1}^{6} + 10 \, k_{1}^{5} k_{2} + 13 \, k_{1}^{4} k_{2}^{2} + 12 \, k_{1}^{3} k_{2}^{3} + 13 \, k_{1}^{2} k_{2}^{4} + 10 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left({\left(k_{1}^{6} - 2 \, k_{1}^{5} k_{2} - k_{1}^{4} k_{2}^{2} + 4 \, k_{1}^{3} k_{2}^{3} - k_{1}^{2} k_{2}^{4} - 2 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left({\left(2 \, k_{1} + 3 \, k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{6} + 2 \, k_{1}^{5} k_{2} - k_{1}^{4} k_{2}^{2} - 4 \, k_{1}^{3} k_{2}^{3} - k_{1}^{2} k_{2}^{4} + 2 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left({\left(k_{1} + 3 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(3 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{6} + 6 \, k_{1}^{5} k_{2} + 15 \, k_{1}^{4} k_{2}^{2} + 20 \, k_{1}^{3} k_{2}^{3} + 15 \, k_{1}^{2} k_{2}^{4} + 6 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left(k_{1} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{6} + 6 \, k_{1}^{5} k_{2} + 15 \, k_{1}^{4} k_{2}^{2} + 20 \, k_{1}^{3} k_{2}^{3} + 15 \, k_{1}^{2} k_{2}^{4} + 6 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left(2 \, k_{1} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} D[0, 1]\left(\alpha\right)\left(x, t_{1}, t_{2}, t_{3}\right) - {\left({\left({\left(3 \, k_{1}^{7} + 10 \, k_{1}^{6} k_{2} + 9 \, k_{1}^{5} k_{2}^{2} - 4 \, k_{1}^{4} k_{2}^{3} - 11 \, k_{1}^{3} k_{2}^{4} - 6 \, k_{1}^{2} k_{2}^{5} - k_{1} k_{2}^{6}\right)} e^{\left({\left(2 \, k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(3 \, k_{1}^{7} + 14 \, k_{1}^{6} k_{2} + 25 \, k_{1}^{5} k_{2}^{2} + 20 \, k_{1}^{4} k_{2}^{3} + 5 \, k_{1}^{3} k_{2}^{4} - 2 \, k_{1}^{2} k_{2}^{5} - k_{1} k_{2}^{6}\right)} e^{\left({\left(k_{1} + k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(\beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left({\left(3 \, k_{1}^{7} + 2 \, k_{1}^{6} k_{2} - 7 \, k_{1}^{5} k_{2}^{2} - 4 \, k_{1}^{4} k_{2}^{3} + 5 \, k_{1}^{3} k_{2}^{4} + 2 \, k_{1}^{2} k_{2}^{5} - k_{1} k_{2}^{6}\right)} e^{\left(2 \, {\left(k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(3 \, k_{1}^{7} + 10 \, k_{1}^{6} k_{2} + 9 \, k_{1}^{5} k_{2}^{2} - 4 \, k_{1}^{4} k_{2}^{3} - 11 \, k_{1}^{3} k_{2}^{4} - 6 \, k_{1}^{2} k_{2}^{5} - k_{1} k_{2}^{6}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left({\left(k_{1}^{7} - 2 \, k_{1}^{6} k_{2} - k_{1}^{5} k_{2}^{2} + 4 \, k_{1}^{4} k_{2}^{3} - k_{1}^{3} k_{2}^{4} - 2 \, k_{1}^{2} k_{2}^{5} + k_{1} k_{2}^{6}\right)} e^{\left({\left(2 \, k_{1} + 3 \, k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(k_{1}^{7} + 2 \, k_{1}^{6} k_{2} - k_{1}^{5} k_{2}^{2} - 4 \, k_{1}^{4} k_{2}^{3} - k_{1}^{3} k_{2}^{4} + 2 \, k_{1}^{2} k_{2}^{5} + k_{1} k_{2}^{6}\right)} e^{\left({\left(k_{1} + 3 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(3 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(k_{1}^{7} + 6 \, k_{1}^{6} k_{2} + 15 \, k_{1}^{5} k_{2}^{2} + 20 \, k_{1}^{4} k_{2}^{3} + 15 \, k_{1}^{3} k_{2}^{4} + 6 \, k_{1}^{2} k_{2}^{5} + k_{1} k_{2}^{6}\right)} e^{\left(k_{1} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{7} + 6 \, k_{1}^{6} k_{2} + 15 \, k_{1}^{5} k_{2}^{2} + 20 \, k_{1}^{4} k_{2}^{3} + 15 \, k_{1}^{3} k_{2}^{4} + 6 \, k_{1}^{2} k_{2}^{5} + k_{1} k_{2}^{6}\right)} e^{\left(2 \, k_{1} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} D[1]\left(\alpha\right)\left(x, t_{1}, t_{2}, t_{3}\right)\right)} D[0]\left(\alpha\right)\left(x, t_{1}, t_{2}, t_{3}\right) + 2 \, {\left({\left({\left({\left(k_{1}^{6} + 2 \, k_{1}^{5} k_{2} - k_{1}^{4} k_{2}^{2} - 4 \, k_{1}^{3} k_{2}^{3} - k_{1}^{2} k_{2}^{4} + 2 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left({\left(3 \, k_{1} + k_{2}\right)} x + 3 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{6} + 6 \, k_{1}^{5} k_{2} + 15 \, k_{1}^{4} k_{2}^{2} + 20 \, k_{1}^{3} k_{2}^{3} + 15 \, k_{1}^{2} k_{2}^{4} + 6 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left(k_{2} x\right)} + {\left(3 \, k_{1}^{6} + 10 \, k_{1}^{5} k_{2} + 13 \, k_{1}^{4} k_{2}^{2} + 12 \, k_{1}^{3} k_{2}^{3} + 13 \, k_{1}^{2} k_{2}^{4} + 10 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(2 \, k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(3 \, k_{1}^{6} + 14 \, k_{1}^{5} k_{2} + 29 \, k_{1}^{4} k_{2}^{2} + 36 \, k_{1}^{3} k_{2}^{3} + 29 \, k_{1}^{2} k_{2}^{4} + 14 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(k_{1} + k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(\beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left({\left(k_{1}^{6} - 2 \, k_{1}^{5} k_{2} - k_{1}^{4} k_{2}^{2} + 4 \, k_{1}^{3} k_{2}^{3} - k_{1}^{2} k_{2}^{4} - 2 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left({\left(3 \, k_{1} + 2 \, k_{2}\right)} x + 3 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{6} + 6 \, k_{1}^{5} k_{2} + 15 \, k_{1}^{4} k_{2}^{2} + 20 \, k_{1}^{3} k_{2}^{3} + 15 \, k_{1}^{2} k_{2}^{4} + 6 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left(2 \, k_{2} x\right)} + {\left(3 \, k_{1}^{6} + 2 \, k_{1}^{5} k_{2} - 3 \, k_{1}^{4} k_{2}^{2} - 4 \, k_{1}^{3} k_{2}^{3} - 3 \, k_{1}^{2} k_{2}^{4} + 2 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left(2 \, {\left(k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(3 \, k_{1}^{6} + 10 \, k_{1}^{5} k_{2} + 13 \, k_{1}^{4} k_{2}^{2} + 12 \, k_{1}^{3} k_{2}^{3} + 13 \, k_{1}^{2} k_{2}^{4} + 10 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} D[1]\left(\beta\right)\left(x, t_{1}, t_{2}, t_{3}\right) - 4 \, {\left({\left({\left(k_{1}^{5} k_{2} + 4 \, k_{1}^{4} k_{2}^{2} + 6 \, k_{1}^{3} k_{2}^{3} + 4 \, k_{1}^{2} k_{2}^{4} + k_{1} k_{2}^{5}\right)} e^{\left({\left(2 \, k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{5} k_{2} + 4 \, k_{1}^{4} k_{2}^{2} + 6 \, k

...

_{1}^{2} k_{2}^{4} + 6 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left(2 \, k_{2} x\right)} + {\left(3 \, k_{1}^{6} + 2 \, k_{1}^{5} k_{2} - 3 \, k_{1}^{4} k_{2}^{2} - 4 \, k_{1}^{3} k_{2}^{3} - 3 \, k_{1}^{2} k_{2}^{4} + 2 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left(2 \, {\left(k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(3 \, k_{1}^{6} + 10 \, k_{1}^{5} k_{2} + 13 \, k_{1}^{4} k_{2}^{2} + 12 \, k_{1}^{3} k_{2}^{3} + 13 \, k_{1}^{2} k_{2}^{4} + 10 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} D[0, 1]\left(\beta\right)\left(x, t_{1}, t_{2}, t_{3}\right) - 4 \, {\left({\left({\left(k_{1}^{5} k_{2} + 4 \, k_{1}^{4} k_{2}^{2} + 6 \, k_{1}^{3} k_{2}^{3} + 4 \, k_{1}^{2} k_{2}^{4} + k_{1} k_{2}^{5}\right)} e^{\left({\left(2 \, k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{5} k_{2} + 4 \, k_{1}^{4} k_{2}^{2} + 6 \, k_{1}^{3} k_{2}^{3} + 4 \, k_{1}^{2} k_{2}^{4} + k_{1} k_{2}^{5}\right)} e^{\left({\left(k_{1} + k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(\beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left({\left(k_{1}^{5} k_{2} - 2 \, k_{1}^{3} k_{2}^{3} + k_{1} k_{2}^{5}\right)} e^{\left(2 \, {\left(k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{5} k_{2} + 4 \, k_{1}^{4} k_{2}^{2} + 6 \, k_{1}^{3} k_{2}^{3} + 4 \, k_{1}^{2} k_{2}^{4} + k_{1} k_{2}^{5}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} D[0, 1]\left(\alpha\right)\left(x, t_{1}, t_{2}, t_{3}\right) + 4 \, {\left({\left({\left(k_{1}^{6} k_{2} + 3 \, k_{1}^{5} k_{2}^{2} + 2 \, k_{1}^{4} k_{2}^{3} - 2 \, k_{1}^{3} k_{2}^{4} - 3 \, k_{1}^{2} k_{2}^{5} - k_{1} k_{2}^{6}\right)} e^{\left({\left(2 \, k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(k_{1}^{6} k_{2} + 5 \, k_{1}^{5} k_{2}^{2} + 10 \, k_{1}^{4} k_{2}^{3} + 10 \, k_{1}^{3} k_{2}^{4} + 5 \, k_{1}^{2} k_{2}^{5} + k_{1} k_{2}^{6}\right)} e^{\left({\left(k_{1} + k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(\beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left({\left(k_{1}^{6} k_{2} + k_{1}^{5} k_{2}^{2} - 2 \, k_{1}^{4} k_{2}^{3} - 2 \, k_{1}^{3} k_{2}^{4} + k_{1}^{2} k_{2}^{5} + k_{1} k_{2}^{6}\right)} e^{\left(2 \, {\left(k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(k_{1}^{6} k_{2} + 3 \, k_{1}^{5} k_{2}^{2} + 2 \, k_{1}^{4} k_{2}^{3} - 2 \, k_{1}^{3} k_{2}^{4} - 3 \, k_{1}^{2} k_{2}^{5} - k_{1} k_{2}^{6}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} D[1]\left(\alpha\right)\left(x, t_{1}, t_{2}, t_{3}\right) - {\left(4 \, {\left({\left({\left(k_{1}^{5} k_{2} + 4 \, k_{1}^{4} k_{2}^{2} + 6 \, k_{1}^{3} k_{2}^{3} + 4 \, k_{1}^{2} k_{2}^{4} + k_{1} k_{2}^{5}\right)} e^{\left({\left(2 \, k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{5} k_{2} + 4 \, k_{1}^{4} k_{2}^{2} + 6 \, k_{1}^{3} k_{2}^{3} + 4 \, k_{1}^{2} k_{2}^{4} + k_{1} k_{2}^{5}\right)} e^{\left({\left(k_{1} + k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(\beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left({\left(k_{1}^{5} k_{2} - 2 \, k_{1}^{3} k_{2}^{3} + k_{1} k_{2}^{5}\right)} e^{\left(2 \, {\left(k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{5} k_{2} + 4 \, k_{1}^{4} k_{2}^{2} + 6 \, k_{1}^{3} k_{2}^{3} + 4 \, k_{1}^{2} k_{2}^{4} + k_{1} k_{2}^{5}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} D[0]\left(\alpha\right)\left(x, t_{1}, t_{2}, t_{3}\right) + {\left({\left(k_{1}^{6} k_{2} + 2 \, k_{1}^{5} k_{2}^{2} - 5 \, k_{1}^{4} k_{2}^{3} - 20 \, k_{1}^{3} k_{2}^{4} - 25 \, k_{1}^{2} k_{2}^{5} - 14 \, k_{1} k_{2}^{6} - 3 \, k_{2}^{7}\right)} e^{\left({\left(k_{1} + k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(k_{1}^{6} k_{2} + 2 \, k_{1}^{5} k_{2}^{2} - k_{1}^{4} k_{2}^{3} - 4 \, k_{1}^{3} k_{2}^{4} - k_{1}^{2} k_{2}^{5} + 2 \, k_{1} k_{2}^{6} + k_{2}^{7}\right)} e^{\left({\left(3 \, k_{1} + k_{2}\right)} x + 3 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{6} k_{2} + 6 \, k_{1}^{5} k_{2}^{2} + 11 \, k_{1}^{4} k_{2}^{3} + 4 \, k_{1}^{3} k_{2}^{4} - 9 \, k_{1}^{2} k_{2}^{5} - 10 \, k_{1} k_{2}^{6} - 3 \, k_{2}^{7}\right)} e^{\left({\left(2 \, k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(k_{1}^{6} k_{2} + 6 \, k_{1}^{5} k_{2}^{2} + 15 \, k_{1}^{4} k_{2}^{3} + 20 \, k_{1}^{3} k_{2}^{4} + 15 \, k_{1}^{2} k_{2}^{5} + 6 \, k_{1} k_{2}^{6} + k_{2}^{7}\right)} e^{\left(k_{2} x\right)}\right)} e^{\left(\beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left({\left(k_{1}^{6} k_{2} - 2 \, k_{1}^{5} k_{2}^{2} - 5 \, k_{1}^{4} k_{2}^{3} + 4 \, k_{1}^{3} k_{2}^{4} + 7 \, k_{1}^{2} k_{2}^{5} - 2 \, k_{1} k_{2}^{6} - 3 \, k_{2}^{7}\right)} e^{\left(2 \, {\left(k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(k_{1}^{6} k_{2} - 2 \, k_{1}^{5} k_{2}^{2} - k_{1}^{4} k_{2}^{3} + 4 \, k_{1}^{3} k_{2}^{4} - k_{1}^{2} k_{2}^{5} - 2 \, k_{1} k_{2}^{6} + k_{2}^{7}\right)} e^{\left({\left(3 \, k_{1} + 2 \, k_{2}\right)} x + 3 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{6} k_{2} + 6 \, k_{1}^{5} k_{2}^{2} + 11 \, k_{1}^{4} k_{2}^{3} + 4 \, k_{1}^{3} k_{2}^{4} - 9 \, k_{1}^{2} k_{2}^{5} - 10 \, k_{1} k_{2}^{6} - 3 \, k_{2}^{7}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(k_{1}^{6} k_{2} + 6 \, k_{1}^{5} k_{2}^{2} + 15 \, k_{1}^{4} k_{2}^{3} + 20 \, k_{1}^{3} k_{2}^{4} + 15 \, k_{1}^{2} k_{2}^{5} + 6 \, k_{1} k_{2}^{6} + k_{2}^{7}\right)} e^{\left(2 \, k_{2} x\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} D[1]\left(\beta\right)\left(x, t_{1}, t_{2}, t_{3}\right)\right)} D[0]\left(\beta\right)\left(x, t_{1}, t_{2}, t_{3}\right) + 2 \, {\left(4 \, {\left({\left({\left(k_{1}^{5} k_{2} + 4 \, k_{1}^{4} k_{2}^{2} + 6 \, k_{1}^{3} k_{2}^{3} + 4 \, k_{1}^{2} k_{2}^{4} + k_{1} k_{2}^{5}\right)} e^{\left({\left(2 \, k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(k_{1}^{5} k_{2} + 4 \, k_{1}^{4} k_{2}^{2} + 6 \, k_{1}^{3} k_{2}^{3} + 4 \, k_{1}^{2} k_{2}^{4} + k_{1} k_{2}^{5}\right)} e^{\left({\left(k_{1} + k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(\beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left({\left(k_{1}^{5} k_{2} - 2 \, k_{1}^{3} k_{2}^{3} + k_{1} k_{2}^{5}\right)} e^{\left(2 \, {\left(k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(k_{1}^{5} k_{2} + 4 \, k_{1}^{4} k_{2}^{2} + 6 \, k_{1}^{3} k_{2}^{3} + 4 \, k_{1}^{2} k_{2}^{4} + k_{1} k_{2}^{5}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} D[0]\left(\alpha\right)\left(x, t_{1}, t_{2}, t_{3}\right)^{2} - 4 \, {\left({\left({\left(k_{1}^{5} k_{2} + 4 \, k_{1}^{4} k_{2}^{2} + 6 \, k_{1}^{3} k_{2}^{3} + 4 \, k_{1}^{2} k_{2}^{4} + k_{1} k_{2}^{5}\right)} e^{\left({\left(2 \, k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{5} k_{2} + 4 \, k_{1}^{4} k_{2}^{2} + 6 \, k_{1}^{3} k_{2}^{3} + 4 \, k_{1}^{2} k_{2}^{4} + k_{1} k_{2}^{5}\right)} e^{\left({\left(k_{1} + k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(\beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left({\left(k_{1}^{5} k_{2} - 2 \, k_{1}^{3} k_{2}^{3} + k_{1} k_{2}^{5}\right)} e^{\left(2 \, {\left(k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{5} k_{2} + 4 \, k_{1}^{4} k_{2}^{2} + 6 \, k_{1}^{3} k_{2}^{3} + 4 \, k_{1}^{2} k_{2}^{4} + k_{1} k_{2}^{5}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} D[0, 0]\left(\alpha\right)\left(x, t_{1}, t_{2}, t_{3}\right) + 8 \, {\left({\left({\left(k_{1}^{6} k_{2} + 3 \, k_{1}^{5} k_{2}^{2} + 2 \, k_{1}^{4} k_{2}^{3} - 2 \, k_{1}^{3} k_{2}^{4} - 3 \, k_{1}^{2} k_{2}^{5} - k_{1} k_{2}^{6}\right)} e^{\left({\left(2 \, k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(k_{1}^{6} k_{2} + 5 \, k_{1}^{5} k_{2}^{2} + 10 \, k_{1}^{4} k_{2}^{3} + 10 \, k_{1}^{3} k_{2}^{4} + 5 \, k_{1}^{2} k_{2}^{5} + k_{1} k_{2}^{6}\right)} e^{\left({\left(k_{1} + k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(\beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left({\left(k_{1}^{6} k_{2} + k_{1}^{5} k_{2}^{2} - 2 \, k_{1}^{4} k_{2}^{3} - 2 \, k_{1}^{3} k_{2}^{4} + k_{1}^{2} k_{2}^{5} + k_{1} k_{2}^{6}\right)} e^{\left(2 \, {\left(k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(k_{1}^{6} k_{2} + 3 \, k_{1}^{5} k_{2}^{2} + 2 \, k_{1}^{4} k_{2}^{3} - 2 \, k_{1}^{3} k_{2}^{4} - 3 \, k_{1}^{2} k_{2}^{5} - k_{1} k_{2}^{6}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} D[0]\left(\alpha\right)\left(x, t_{1}, t_{2}, t_{3}\right) + {\left({\left(k_{1}^{6} k_{2}^{2} + 2 \, k_{1}^{5} k_{2}^{3} - k_{1}^{4} k_{2}^{4} - 4 \, k_{1}^{3} k_{2}^{5} - k_{1}^{2} k_{2}^{6} + 2 \, k_{1} k_{2}^{7} + k_{2}^{8}\right)} e^{\left({\left(3 \, k_{1} + k_{2}\right)} x + 3 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{6} k_{2}^{2} + 6 \, k_{1}^{5} k_{2}^{3} + 15 \, k_{1}^{4} k_{2}^{4} + 20 \, k_{1}^{3} k_{2}^{5} + 15 \, k_{1}^{2} k_{2}^{6} + 6 \, k_{1} k_{2}^{7} + k_{2}^{8}\right)} e^{\left(k_{2} x\right)} - {\left(4 \, k_{1}^{7} k_{2} + 21 \, k_{1}^{6} k_{2}^{2} + 42 \, k_{1}^{5} k_{2}^{3} + 35 \, k_{1}^{4} k_{2}^{4} - 21 \, k_{1}^{2} k_{2}^{6} - 14 \, k_{1} k_{2}^{7} - 3 \, k_{2}^{8}\right)} e^{\left({\left(k_{1} + k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(4 \, k_{1}^{7} k_{2} + 11 \, k_{1}^{6} k_{2}^{2} + 2 \, k_{1}^{5} k_{2}^{3} - 19 \, k_{1}^{4} k_{2}^{4} - 16 \, k_{1}^{3} k_{2}^{5} + 5 \, k_{1}^{2} k_{2}^{6} + 10 \, k_{1} k_{2}^{7} + 3 \, k_{2}^{8}\right)} e^{\left({\left(2 \, k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(\beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left({\left(k_{1}^{6} k_{2}^{2} - 2 \, k_{1}^{5} k_{2}^{3} - k_{1}^{4} k_{2}^{4} + 4 \, k_{1}^{3} k_{2}^{5} - k_{1}^{2} k_{2}^{6} - 2 \, k_{1} k_{2}^{7} + k_{2}^{8}\right)} e^{\left({\left(3 \, k_{1} + 2 \, k_{2}\right)} x + 3 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{6} k_{2}^{2} + 6 \, k_{1}^{5} k_{2}^{3} + 15 \, k_{1}^{4} k_{2}^{4} + 20 \, k_{1}^{3} k_{2}^{5} + 15 \, k_{1}^{2} k_{2}^{6} + 6 \, k_{1} k_{2}^{7} + k_{2}^{8}\right)} e^{\left(2 \, k_{2} x\right)} - {\left(4 \, k_{1}^{7} k_{2} + 5 \, k_{1}^{6} k_{2}^{2} - 10 \, k_{1}^{5} k_{2}^{3} - 13 \, k_{1}^{4} k_{2}^{4} + 8 \, k_{1}^{3} k_{2}^{5} + 11 \, k_{1}^{2} k_{2}^{6} - 2 \, k_{1} k_{2}^{7} - 3 \, k_{2}^{8}\right)} e^{\left(2 \, {\left(k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(4 \, k_{1}^{7} k_{2} + 11 \, k_{1}^{6} k_{2}^{2} + 2 \, k_{1}^{5} k_{2}^{3} - 19 \, k_{1}^{4} k_{2}^{4} - 16 \, k_{1}^{3} k_{2}^{5} + 5 \, k_{1}^{2} k_{2}^{6} + 10 \, k_{1} k_{2}^{7} + 3 \, k_{2}^{8}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} D[1]\left(\beta\right)\left(x, t_{1}, t_{2}, t_{3}\right) + 2 \, {\left({\left(3 \, {\left(k_{1}^{6} + 2 \, k_{1}^{5} k_{2} - k_{1}^{4} k_{2}^{2} - 4 \, k_{1}^{3} k_{2}^{3} - k_{1}^{2} k_{2}^{4} + 2 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left({\left(3 \, k_{1} + k_{2}\right)} x + 3 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + 2 \, {\left(3 \, k_{1}^{6} + 10 \, k_{1}^{5} k_{2} + 13 \, k_{1}^{4} k_{2}^{2} + 12 \, k_{1}^{3} k_{2}^{3} + 13 \, k_{1}^{2} k_{2}^{4} + 10 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(2 \, k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(3 \, k_{1}^{6} + 14 \, k_{1}^{5} k_{2} + 29 \, k_{1}^{4} k_{2}^{2} + 36 \, k_{1}^{3} k_{2}^{3} + 29 \, k_{1}^{2} k_{2}^{4} + 14 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(k_{1} + k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(\beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(3 \, {\left(k_{1}^{6} - 2 \, k_{1}^{5} k_{2} - k_{1}^{4} k_{2}^{2} + 4 \, k_{1}^{3} k_{2}^{3} - k_{1}^{2} k_{2}^{4} - 2 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left({\left(3 \, k_{1} + 2 \, k_{2}\right)} x + 3 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + 2 \, {\left(3 \, k_{1}^{6} + 2 \, k_{1}^{5} k_{2} - 3 \, k_{1}^{4} k_{2}^{2} - 4 \, k_{1}^{3} k_{2}^{3} - 3 \, k_{1}^{2} k_{2}^{4} + 2 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left(2 \, {\left(k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(3 \, k_{1}^{6} + 10 \, k_{1}^{5} k_{2} + 13 \, k_{1}^{4} k_{2}^{2} + 12 \, k_{1}^{3} k_{2}^{3} + 13 \, k_{1}^{2} k_{2}^{4} + 10 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left({\left(k_{1}^{6} - 6 \, k_{1}^{5} k_{2} + 15 \, k_{1}^{4} k_{2}^{2} - 20 \, k_{1}^{3} k_{2}^{3} + 15 \, k_{1}^{2} k_{2}^{4} - 6 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left(3 \, {\left(k_{1} + k_{2}\right)} x + 3 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + 2 \, {\left(k_{1}^{6} - 2 \, k_{1}^{5} k_{2} - k_{1}^{4} k_{2}^{2} + 4 \, k_{1}^{3} k_{2}^{3} - k_{1}^{2} k_{2}^{4} - 2 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left({\left(2 \, k_{1} + 3 \, k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{6} + 2 \, k_{1}^{5} k_{2} - k_{1}^{4} k_{2}^{2} - 4 \, k_{1}^{3} k_{2}^{3} - k_{1}^{2} k_{2}^{4} + 2 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left({\left(k_{1} + 3 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(3 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{6} + 6 \, k_{1}^{5} k_{2} + 15 \, k_{1}^{4} k_{2}^{2} + 20 \, k_{1}^{3} k_{2}^{3} + 15 \, k_{1}^{2} k_{2}^{4} + 6 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left(k_{1} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + 2 \, {\left(k_{1}^{6} + 6 \, k_{1}^{5} k_{2} + 15 \, k_{1}^{4} k_{2}^{2} + 20 \, k_{1}^{3} k_{2}^{3} + 15 \, k_{1}^{2} k_{2}^{4} + 6 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left(2 \, k_{1} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{6} + 6 \, k_{1}^{5} k_{2} + 15 \, k_{1}^{4} k_{2}^{2} + 20 \, k_{1}^{3} k_{2}^{3} + 15 \, k_{1}^{2} k_{2}^{4} + 6 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left(3 \, k_{1} x + 3 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} D[0, 0, 1]\left(\alpha\right)\left(x, t_{1}, t_{2}, t_{3}\right)

full_output.txt

RHSt1.numerator()

WARNING: Output truncated!  
full_output.txt



\newcommand{\Bold}[1]{\mathbf{#1}}2 \, {\left({\left({\left(k_{1}^{6} + 2 \, k_{1}^{5} k_{2} - k_{1}^{4} k_{2}^{2} - 4 \, k_{1}^{3} k_{2}^{3} - k_{1}^{2} k_{2}^{4} + 2 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left({\left(3 \, k_{1} + k_{2}\right)} x + 3 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{6} + 6 \, k_{1}^{5} k_{2} + 15 \, k_{1}^{4} k_{2}^{2} + 20 \, k_{1}^{3} k_{2}^{3} + 15 \, k_{1}^{2} k_{2}^{4} + 6 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left(k_{2} x\right)} + {\left(3 \, k_{1}^{6} + 10 \, k_{1}^{5} k_{2} + 13 \, k_{1}^{4} k_{2}^{2} + 12 \, k_{1}^{3} k_{2}^{3} + 13 \, k_{1}^{2} k_{2}^{4} + 10 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(2 \, k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(3 \, k_{1}^{6} + 14 \, k_{1}^{5} k_{2} + 29 \, k_{1}^{4} k_{2}^{2} + 36 \, k_{1}^{3} k_{2}^{3} + 29 \, k_{1}^{2} k_{2}^{4} + 14 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(k_{1} + k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(\beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left({\left(k_{1}^{6} - 2 \, k_{1}^{5} k_{2} - k_{1}^{4} k_{2}^{2} + 4 \, k_{1}^{3} k_{2}^{3} - k_{1}^{2} k_{2}^{4} - 2 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left({\left(3 \, k_{1} + 2 \, k_{2}\right)} x + 3 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{6} + 6 \, k_{1}^{5} k_{2} + 15 \, k_{1}^{4} k_{2}^{2} + 20 \, k_{1}^{3} k_{2}^{3} + 15 \, k_{1}^{2} k_{2}^{4} + 6 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left(2 \, k_{2} x\right)} + {\left(3 \, k_{1}^{6} + 2 \, k_{1}^{5} k_{2} - 3 \, k_{1}^{4} k_{2}^{2} - 4 \, k_{1}^{3} k_{2}^{3} - 3 \, k_{1}^{2} k_{2}^{4} + 2 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left(2 \, {\left(k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(3 \, k_{1}^{6} + 10 \, k_{1}^{5} k_{2} + 13 \, k_{1}^{4} k_{2}^{2} + 12 \, k_{1}^{3} k_{2}^{3} + 13 \, k_{1}^{2} k_{2}^{4} + 10 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} D[0]\left(\beta\right)\left(x, t_{1}, t_{2}, t_{3}\right)^{5} - 2 \, {\left({\left({\left(3 \, k_{1}^{6} + 10 \, k_{1}^{5} k_{2} + 13 \, k_{1}^{4} k_{2}^{2} + 12 \, k_{1}^{3} k_{2}^{3} + 13 \, k_{1}^{2} k_{2}^{4} + 10 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(2 \, k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(3 \, k_{1}^{6} + 14 \, k_{1}^{5} k_{2} + 29 \, k_{1}^{4} k_{2}^{2} + 36 \, k_{1}^{3} k_{2}^{3} + 29 \, k_{1}^{2} k_{2}^{4} + 14 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(k_{1} + k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(\beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left({\left(3 \, k_{1}^{6} + 2 \, k_{1}^{5} k_{2} - 3 \, k_{1}^{4} k_{2}^{2} - 4 \, k_{1}^{3} k_{2}^{3} - 3 \, k_{1}^{2} k_{2}^{4} + 2 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left(2 \, {\left(k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(3 \, k_{1}^{6} + 10 \, k_{1}^{5} k_{2} + 13 \, k_{1}^{4} k_{2}^{2} + 12 \, k_{1}^{3} k_{2}^{3} + 13 \, k_{1}^{2} k_{2}^{4} + 10 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left({\left(k_{1}^{6} - 2 \, k_{1}^{5} k_{2} - k_{1}^{4} k_{2}^{2} + 4 \, k_{1}^{3} k_{2}^{3} - k_{1}^{2} k_{2}^{4} - 2 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left({\left(2 \, k_{1} + 3 \, k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(k_{1}^{6} + 2 \, k_{1}^{5} k_{2} - k_{1}^{4} k_{2}^{2} - 4 \, k_{1}^{3} k_{2}^{3} - k_{1}^{2} k_{2}^{4} + 2 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left({\left(k_{1} + 3 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(3 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(k_{1}^{6} + 6 \, k_{1}^{5} k_{2} + 15 \, k_{1}^{4} k_{2}^{2} + 20 \, k_{1}^{3} k_{2}^{3} + 15 \, k_{1}^{2} k_{2}^{4} + 6 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left(k_{1} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{6} + 6 \, k_{1}^{5} k_{2} + 15 \, k_{1}^{4} k_{2}^{2} + 20 \, k_{1}^{3} k_{2}^{3} + 15 \, k_{1}^{2} k_{2}^{4} + 6 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left(2 \, k_{1} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} D[0]\left(\alpha\right)\left(x, t_{1}, t_{2}, t_{3}\right)^{5} - 10 \, {\left(4 \, {\left({\left({\left(k_{1}^{5} k_{2} + 4 \, k_{1}^{4} k_{2}^{2} + 6 \, k_{1}^{3} k_{2}^{3} + 4 \, k_{1}^{2} k_{2}^{4} + k_{1} k_{2}^{5}\right)} e^{\left({\left(2 \, k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{5} k_{2} + 4 \, k_{1}^{4} k_{2}^{2} + 6 \, k_{1}^{3} k_{2}^{3} + 4 \, k_{1}^{2} k_{2}^{4} + k_{1} k_{2}^{5}\right)} e^{\left({\left(k_{1} + k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(\beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left({\left(k_{1}^{5} k_{2} - 2 \, k_{1}^{3} k_{2}^{3} + k_{1} k_{2}^{5}\right)} e^{\left(2 \, {\left(k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{5} k_{2} + 4 \, k_{1}^{4} k_{2}^{2} + 6 \, k_{1}^{3} k_{2}^{3} + 4 \, k_{1}^{2} k_{2}^{4} + k_{1} k_{2}^{5}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} D[0]\left(\alpha\right)\left(x, t_{1}, t_{2}, t_{3}\right) + {\left({\left(k_{1}^{6} k_{2} + 2 \, k_{1}^{5} k_{2}^{2} - 5 \, k_{1}^{4} k_{2}^{3} - 20 \, k_{1}^{3} k_{2}^{4} - 25 \, k_{1}^{2} k_{2}^{5} - 14 \, k_{1} k_{2}^{6} - 3 \, k_{2}^{7}\right)} e^{\left({\left(k_{1} + k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(k_{1}^{6} k_{2} + 2 \, k_{1}^{5} k_{2}^{2} - k_{1}^{4} k_{2}^{3} - 4 \, k_{1}^{3} k_{2}^{4} - k_{1}^{2} k_{2}^{5} + 2 \, k_{1} k_{2}^{6} + k_{2}^{7}\right)} e^{\left({\left(3 \, k_{1} + k_{2}\right)} x + 3 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{6} k_{2} + 6 \, k_{1}^{5} k_{2}^{2} + 11 \, k_{1}^{4} k_{2}^{3} + 4 \, k_{1}^{3} k_{2}^{4} - 9 \, k_{1}^{2} k_{2}^{5} - 10 \, k_{1} k_{2}^{6} - 3 \, k_{2}^{7}\right)} e^{\left({\left(2 \, k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(k_{1}^{6} k_{2} + 6 \, k_{1}^{5} k_{2}^{2} + 15 \, k_{1}^{4} k_{2}^{3} + 20 \, k_{1}^{3} k_{2}^{4} + 15 \, k_{1}^{2} k_{2}^{5} + 6 \, k_{1} k_{2}^{6} + k_{2}^{7}\right)} e^{\left(k_{2} x\right)}\right)} e^{\left(\beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left({\left(k_{1}^{6} k_{2} - 2 \, k_{1}^{5} k_{2}^{2} - 5 \, k_{1}^{4} k_{2}^{3} + 4 \, k_{1}^{3} k_{2}^{4} + 7 \, k_{1}^{2} k_{2}^{5} - 2 \, k_{1} k_{2}^{6} - 3 \, k_{2}^{7}\right)} e^{\left(2 \, {\left(k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(k_{1}^{6} k_{2} - 2 \, k_{1}^{5} k_{2}^{2} - k_{1}^{4} k_{2}^{3} + 4 \, k_{1}^{3} k_{2}^{4} - k_{1}^{2} k_{2}^{5} - 2 \, k_{1} k_{2}^{6} + k_{2}^{7}\right)} e^{\left({\left(3 \, k_{1} + 2 \, k_{2}\right)} x + 3 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{6} k_{2} + 6 \, k_{1}^{5} k_{2}^{2} + 11 \, k_{1}^{4} k_{2}^{3} + 4 \, k_{1}^{3} k_{2}^{4} - 9 \, k_{1}^{2} k_{2}^{5} - 10 \, k_{1} k_{2}^{6} - 3 \, k_{2}^{7}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(k_{1}^{6} k_{2} + 6 \, k_{1}^{5} k_{2}^{2} + 15 \, k_{1}^{4} k_{2}^{3} + 20 \, k_{1}^{3} k_{2}^{4} + 15 \, k_{1}^{2} k_{2}^{5} + 6 \, k_{1} k_{2}^{6} + k_{2}^{7}\right)} e^{\left(2 \, k_{2} x\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} D[0]\left(\beta\right)\left(x, t_{1}, t_{2}, t_{3}\right)^{4} - 10 \, {\left({\left({\left(3 \, k_{1}^{7} + 10 \, k_{1}^{6} k_{2} + 9 \, k_{1}^{5} k_{2}^{2} - 4 \, k_{1}^{4} k_{2}^{3} - 11 \, k_{1}^{3} k_{2}^{4} - 6 \, k_{1}^{2} k_{2}^{5} - k_{1} k_{2}^{6}\right)} e^{\left({\left(2 \, k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(3 \, k_{1}^{7} + 14 \, k_{1}^{6} k_{2} + 25 \, k_{1}^{5} k_{2}^{2} + 20 \, k_{1}^{4} k_{2}^{3} + 5 \, k_{1}^{3} k_{2}^{4} - 2 \, k_{1}^{2} k_{2}^{5} - k_{1} k_{2}^{6}\right)} e^{\left({\left(k_{1} + k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(\beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left({\left(3 \, k_{1}^{7} + 2 \, k_{1}^{6} k_{2} - 7 \, k_{1}^{5} k_{2}^{2} - 4 \, k_{1}^{4} k_{2}^{3} + 5 \, k_{1}^{3} k_{2}^{4} + 2 \, k_{1}^{2} k_{2}^{5} - k_{1} k_{2}^{6}\right)} e^{\left(2 \, {\left(k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(3 \, k_{1}^{7} + 10 \, k_{1}^{6} k_{2} + 9 \, k_{1}^{5} k_{2}^{2} - 4 \, k_{1}^{4} k_{2}^{3} - 11 \, k_{1}^{3} k_{2}^{4} - 6 \, k_{1}^{2} k_{2}^{5} - k_{1} k_{2}^{6}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left({\left(k_{1}^{7} - 2 \, k_{1}^{6} k_{2} - k_{1}^{5} k_{2}^{2} + 4 \, k_{1}^{4} k_{2}^{3} - k_{1}^{3} k_{2}^{4} - 2 \, k_{1}^{2} k_{2}^{5} + k_{1} k_{2}^{6}\right)} e^{\left({\left(2 \, k_{1} + 3 \, k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(k_{1}^{7} + 2 \, k_{1}^{6} k_{2} - k_{1}^{5} k_{2}^{2} - 4 \, k_{1}^{4} k_{2}^{3} - k_{1}^{3} k_{2}^{4} + 2 \, k_{1}^{2} k_{2}^{5} + k_{1} k_{2}^{6}\right)} e^{\left({\left(k_{1} + 3 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(3 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(k_{1}^{7} + 6 \, k_{1}^{6} k_{2} + 15 \, k_{1}^{5} k_{2}^{2} + 20 \, k_{1}^{4} k_{2}^{3} + 15 \, k_{1}^{3} k_{2}^{4} + 6 \, k_{1}^{2} k_{2}^{5} + k_{1} k_{2}^{6}\right)} e^{\left(k_{1} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{7} + 6 \, k_{1}^{6} k_{2} + 15 \, k_{1}^{5} k_{2}^{2} + 20 \, k_{1}^{4} k_{2}^{3} + 15 \, k_{1}^{3} k_{2}^{4} + 6 \, k_{1}^{2} k_{2}^{5} + k_{1} k_{2}^{6}\right)} e^{\left(2 \, k_{1} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} D[0]\left(\alpha\right)\left(x, t_{1}, t_{2}, t_{3}\right)^{4} - 4 \, {\left({\left({\left(15 \, k_{1}^{8} + 50 \, k_{1}^{7} k_{2} + 31 \, k_{1}^{6} k_{2}^{2} - 68 \, k_{1}^{5} k_{2}^{3} - 101 \, k_{1}^{4} k_{2}^{4} - 14 \, k_{1}^{3} k_{2}^{5} + 49 \, k_{1}^{2} k_{2}^{6} + 32 \, k_{1} k_{2}^{7} + 6 \, k_{2}^{8}\right)} e^{\left({\left(2 \, k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(15 \, k_{1}^{8} + 70 \, k_{1}^{7} k_{2} + 111 \, k_{1}^{6} k_{2}^{2} + 36 \, k_{1}^{5} k_{2}^{3} - 85 \, k_{1}^{4} k_{2}^{4} - 90 \, k_{1}^{3} k_{2}^{5} - 15 \, k_{1}^{2} k_{2}^{6} + 16 \, k_{1} k_{2}^{7} + 6 \, k_{2}^{8}\right)} e^{\left({\left(k_{1} + k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(\beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left({\left(15 \, k_{1}^{8} + 10 \, k_{1}^{7} k_{2} - 49 \, k_{1}^{6} k_{2}^{2} - 28 \, k_{1}^{5} k_{2}^{3} + 59 \, k_{1}^{4} k_{2}^{4} + 26 \, k_{1}^{3} k_{2}^{5} - 31 \, k_{1}^{2} k_{2}^{6} - 8 \, k_{1} k_{2}^{7} + 6 \, k_{2}^{8}\right)} e^{\left(2 \, {\left(k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(15 \, k_{1}^{8} + 50 \, k_{1}^{7} k_{2} + 31 \, k_{1}^{6} k_{2}^{2} - 68 \, k_{1}^{5} k_{2}^{3} - 101 \, k_{1}^{4} k_{2}^{4} - 14 \, k_{1}^{3} k_{2}^{5} + 49 \, k_{1}^{2} k_{2}^{6} + 32 \, k_{1} k_{2}^{7} + 6 \, k_{2}^{8}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + 5 \, {\left({\left(k_{1}^{8} - 2 \, k_{1}^{7} k_{2} - k_{1}^{6} k_{2}^{2} + 4 \, k_{1}^{5} k_{2}^{3} - k_{1}^{4} k_{2}^{4} - 2 \, k_{1}^{3} k_{2}^{5} + k_{1}^{2} k_{2}^{6}\right)} e^{\left({\left(2 \, k_{1} + 3 \, k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(k_{1}^{8} + 2 \, k_{1}^{7} k_{2} - k_{1}^{6} k_{2}^{2} - 4 \, k_{1}^{5} k_{2}^{3} - k_{1}^{4} k_{2}^{4} + 2 \, k_{1}^{3} k_{2}^{5} + k_{1}^{2} k_{2}^{6}\right)} e^{\left({\left(k_{1} + 3 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(3 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - 5 \, {\left(k_{1}^{8} + 6 \, k_{1}^{7} k_{2} + 15 \, k_{1}^{6} k_{2}^{2} + 20 \, k_{1}^{5} k_{2}^{3} + 15 \, k_{1}^{4} k_{2}^{4} + 6 \, k_{1}^{3} k_{2}^{5} + k_{1}^{2} k_{2}^{6}\right)} e^{\left(k_{1} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + 5 \, {\left(k_{1}^{8} + 6 \, k_{1}^{7} k_{2} + 15 \, k_{1}^{6} k_{2}^{2} + 20 \, k_{1}^{5} k_{2}^{3} + 15 \, k_{1}^{4} k_{2}^{4} + 6 \, k_{1}^{3} k_{2}^{5} + k_{1}^{2} k_{2}^{6}\right)} e^{\left(2 \, k_{1} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} D[0]\left(\alpha\right)\left(x, t_{1}, t_{2}, t_{3}\right)^{3} - 4 \, {\left(2 \, {\left({\left({\left(3 \, k_{1}^{6} - 4 \, k_{1}^{5} k_{2} - 3 \, k_{1}^{4} k_{2}^{2} + 8 \, k_{1}^{3} k_{2}^{3} - 3 \, k_{1}^{2} k_{2}^{4} - 4 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left(2 \, {\left(k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(3 \, k_{1}^{6} + 16 \, k_{1}^{5} k_{2} + 37 \, k_{1}^{4} k_{2}^{2} + 48 \, k_{1}^{3} k_{2}^{3} + 37 \, k_{1}^{2} k_{2}^{4} + 16 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left({\left(3 \, k_{1}^{6} + 8 \, k_{1}^{5} k_{2} + 5 \, k_{1}^{4} k_{2}^{2} + 5 \, k_{1}^{2} k_{2}^{4} + 8 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(k_{1} + k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(3 \, k_{1}^{6} + 16 \, k_{1}^{5} k_{2} + 37 \, k_{1}^{4} k_{2}^{2} + 48 \, k_{1}^{3} k_{2}^{3} + 37 \, k_{1}^{2} k_{2}^{4} + 16 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(2 \, k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(\beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} D[0]\left(\alpha\right)\left(x, t_{1}, t_{2}, t_{3}\right)^{2} + 2 \, {\left({\left(3 \, {\left(k_{1}^{6} - 2 \, k_{1}^{5} k_{2} - k_{1}^{4} k_{2}^{2} + 4 \, k_{1}^{3} k_{2}^{3} - k_{1}^{2} k_{2}^{4} - 2 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left({\left(3 \, k_{1} + 2 \, k_{2}\right)} x + 3 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + 2 \, {\left(3 \, k_{1}^{6} + 5 \, k_{1}^{5} k_{2} - 3 \, k_{1}^{4} k_{2}^{2} - 10 \, k_{1}^{3} k_{2}^{3} - 3 \, k_{1}^{2} k_{2}^{4} + 5 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left(2 \, {\left(k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(3 \, k_{1}^{6} + 16 \, k_{1}^{5} k_{2} + 37 \, k_{1}^{4} k_{2}^{2} + 48 \, k_{1}^{3} k_{2}^{3} + 37 \, k_{1}^{2} k_{2}^{4} + 16 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left({\left(3 \, k_{1}^{6} + 8 \, k_{1}^{5} k_{2} + 5 \, k_{1}^{4} k_{2}^{2} + 5 \, k_{1}^{2} k_{2}^{4} + 8 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(k_{1} + k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + 3 \, {\left(k_{1}^{6} + 2 \, k_{1}^{5} k_{2} - k_{1}^{4} k_{2}^{2} - 4 \, k_{1}^{3} k_{2}^{3} - k_{1}^{2} k_{2}^{4} + 2 \, k_{1} k_{2}^{5} + 

...

, t_{2}, t_{3}\right)\right)} - {\left(3 \, k_{1}^{8} + 10 \, k_{1}^{7} k_{2} + 5 \, k_{1}^{6} k_{2}^{2} - 16 \, k_{1}^{5} k_{2}^{3} - 19 \, k_{1}^{4} k_{2}^{4} + 2 \, k_{1}^{3} k_{2}^{5} + 11 \, k_{1}^{2} k_{2}^{6} + 4 \, k_{1} k_{2}^{7}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left({\left(3 \, k_{1}^{8} + 14 \, k_{1}^{7} k_{2} + 21 \, k_{1}^{6} k_{2}^{2} - 35 \, k_{1}^{4} k_{2}^{4} - 42 \, k_{1}^{3} k_{2}^{5} - 21 \, k_{1}^{2} k_{2}^{6} - 4 \, k_{1} k_{2}^{7}\right)} e^{\left({\left(k_{1} + k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(3 \, k_{1}^{8} + 10 \, k_{1}^{7} k_{2} + 5 \, k_{1}^{6} k_{2}^{2} - 16 \, k_{1}^{5} k_{2}^{3} - 19 \, k_{1}^{4} k_{2}^{4} + 2 \, k_{1}^{3} k_{2}^{5} + 11 \, k_{1}^{2} k_{2}^{6} + 4 \, k_{1} k_{2}^{7}\right)} e^{\left({\left(2 \, k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(\beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + 3 \, {\left({\left(k_{1}^{8} - 2 \, k_{1}^{7} k_{2} - k_{1}^{6} k_{2}^{2} + 4 \, k_{1}^{5} k_{2}^{3} - k_{1}^{4} k_{2}^{4} - 2 \, k_{1}^{3} k_{2}^{5} + k_{1}^{2} k_{2}^{6}\right)} e^{\left({\left(2 \, k_{1} + 3 \, k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(k_{1}^{8} + 2 \, k_{1}^{7} k_{2} - k_{1}^{6} k_{2}^{2} - 4 \, k_{1}^{5} k_{2}^{3} - k_{1}^{4} k_{2}^{4} + 2 \, k_{1}^{3} k_{2}^{5} + k_{1}^{2} k_{2}^{6}\right)} e^{\left({\left(k_{1} + 3 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(3 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} D[0]\left(\alpha\right)\left(x, t_{1}, t_{2}, t_{3}\right) + {\left(5 \, {\left(k_{1}^{6} k_{2}^{3} + 2 \, k_{1}^{5} k_{2}^{4} - k_{1}^{4} k_{2}^{5} - 4 \, k_{1}^{3} k_{2}^{6} - k_{1}^{2} k_{2}^{7} + 2 \, k_{1} k_{2}^{8} + k_{2}^{9}\right)} e^{\left({\left(3 \, k_{1} + k_{2}\right)} x + 3 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + 5 \, {\left(k_{1}^{6} k_{2}^{3} + 6 \, k_{1}^{5} k_{2}^{4} + 15 \, k_{1}^{4} k_{2}^{5} + 20 \, k_{1}^{3} k_{2}^{6} + 15 \, k_{1}^{2} k_{2}^{7} + 6 \, k_{1} k_{2}^{8} + k_{2}^{9}\right)} e^{\left(k_{2} x\right)} - {\left(6 \, k_{1}^{9} + 14 \, k_{1}^{8} k_{2} - 22 \, k_{1}^{7} k_{2}^{2} - 81 \, k_{1}^{6} k_{2}^{3} - 24 \, k_{1}^{5} k_{2}^{4} + 105 \, k_{1}^{4} k_{2}^{5} + 90 \, k_{1}^{3} k_{2}^{6} - 23 \, k_{1}^{2} k_{2}^{7} - 50 \, k_{1} k_{2}^{8} - 15 \, k_{2}^{9}\right)} e^{\left({\left(2 \, k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(6 \, k_{1}^{9} + 34 \, k_{1}^{8} k_{2} + 58 \, k_{1}^{7} k_{2}^{2} - 15 \, k_{1}^{6} k_{2}^{3} - 160 \, k_{1}^{5} k_{2}^{4} - 169 \, k_{1}^{4} k_{2}^{5} - 6 \, k_{1}^{3} k_{2}^{6} + 103 \, k_{1}^{2} k_{2}^{7} + 70 \, k_{1} k_{2}^{8} + 15 \, k_{2}^{9}\right)} e^{\left({\left(k_{1} + k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(\beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left({\left(k_{1}^{6} k_{2}^{3} - 2 \, k_{1}^{5} k_{2}^{4} - k_{1}^{4} k_{2}^{5} + 4 \, k_{1}^{3} k_{2}^{6} - k_{1}^{2} k_{2}^{7} - 2 \, k_{1} k_{2}^{8} + k_{2}^{9}\right)} e^{\left({\left(3 \, k_{1} + 2 \, k_{2}\right)} x + 3 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{6} k_{2}^{3} + 6 \, k_{1}^{5} k_{2}^{4} + 15 \, k_{1}^{4} k_{2}^{5} + 20 \, k_{1}^{3} k_{2}^{6} + 15 \, k_{1}^{2} k_{2}^{7} + 6 \, k_{1} k_{2}^{8} + k_{2}^{9}\right)} e^{\left(2 \, k_{2} x\right)} + {\left(12 \, k_{1}^{9} + 2 \, k_{1}^{8} k_{2} - 60 \, k_{1}^{7} k_{2}^{2} - 31 \, k_{1}^{6} k_{2}^{3} + 86 \, k_{1}^{5} k_{2}^{4} + 59 \, k_{1}^{4} k_{2}^{5} - 40 \, k_{1}^{3} k_{2}^{6} - 33 \, k_{1}^{2} k_{2}^{7} + 2 \, k_{1} k_{2}^{8} + 3 \, k_{2}^{9}\right)} e^{\left(2 \, {\left(k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(12 \, k_{1}^{9} + 46 \, k_{1}^{8} k_{2} + 28 \, k_{1}^{7} k_{2}^{2} - 81 \, k_{1}^{6} k_{2}^{3} - 102 \, k_{1}^{5} k_{2}^{4} + 21 \, k_{1}^{4} k_{2}^{5} + 72 \, k_{1}^{3} k_{2}^{6} + 17 \, k_{1}^{2} k_{2}^{7} - 10 \, k_{1} k_{2}^{8} - 3 \, k_{2}^{9}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + 6 \, {\left(3 \, {\left({\left(k_{1}^{7} - 2 \, k_{1}^{6} k_{2} - k_{1}^{5} k_{2}^{2} + 4 \, k_{1}^{4} k_{2}^{3} - k_{1}^{3} k_{2}^{4} - 2 \, k_{1}^{2} k_{2}^{5} + k_{1} k_{2}^{6}\right)} e^{\left({\left(2 \, k_{1} + 3 \, k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{7} + 2 \, k_{1}^{6} k_{2} - k_{1}^{5} k_{2}^{2} - 4 \, k_{1}^{4} k_{2}^{3} - k_{1}^{3} k_{2}^{4} + 2 \, k_{1}^{2} k_{2}^{5} + k_{1} k_{2}^{6}\right)} e^{\left({\left(k_{1} + 3 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(3 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(3 \, {\left(k_{1}^{6} k_{2} + 2 \, k_{1}^{5} k_{2}^{2} - k_{1}^{4} k_{2}^{3} - 4 \, k_{1}^{3} k_{2}^{4} - k_{1}^{2} k_{2}^{5} + 2 \, k_{1} k_{2}^{6} + k_{2}^{7}\right)} e^{\left({\left(3 \, k_{1} + k_{2}\right)} x + 3 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(3 \, k_{1}^{7} + 10 \, k_{1}^{6} k_{2} + 3 \, k_{1}^{5} k_{2}^{2} - 22 \, k_{1}^{4} k_{2}^{3} - 23 \, k_{1}^{3} k_{2}^{4} + 6 \, k_{1}^{2} k_{2}^{5} + 17 \, k_{1} k_{2}^{6} + 6 \, k_{2}^{7}\right)} e^{\left({\left(2 \, k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(3 \, k_{1}^{7} + 11 \, k_{1}^{6} k_{2} + 13 \, k_{1}^{5} k_{2}^{2} + 5 \, k_{1}^{4} k_{2}^{3} + 5 \, k_{1}^{3} k_{2}^{4} + 13 \, k_{1}^{2} k_{2}^{5} + 11 \, k_{1} k_{2}^{6} + 3 \, k_{2}^{7}\right)} e^{\left({\left(k_{1} + k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(\beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(3 \, {\left(k_{1}^{6} k_{2} - 2 \, k_{1}^{5} k_{2}^{2} - k_{1}^{4} k_{2}^{3} + 4 \, k_{1}^{3} k_{2}^{4} - k_{1}^{2} k_{2}^{5} - 2 \, k_{1} k_{2}^{6} + k_{2}^{7}\right)} e^{\left({\left(3 \, k_{1} + 2 \, k_{2}\right)} x + 3 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + 2 \, {\left(3 \, k_{1}^{7} + 2 \, k_{1}^{6} k_{2} - 4 \, k_{1}^{5} k_{2}^{2} - k_{1}^{4} k_{2}^{3} - k_{1}^{3} k_{2}^{4} - 4 \, k_{1}^{2} k_{2}^{5} + 2 \, k_{1} k_{2}^{6} + 3 \, k_{2}^{7}\right)} e^{\left(2 \, {\left(k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(6 \, k_{1}^{7} + 17 \, k_{1}^{6} k_{2} + 6 \, k_{1}^{5} k_{2}^{2} - 23 \, k_{1}^{4} k_{2}^{3} - 22 \, k_{1}^{3} k_{2}^{4} + 3 \, k_{1}^{2} k_{2}^{5} + 10 \, k_{1} k_{2}^{6} + 3 \, k_{2}^{7}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(2 \, {\left({\left(3 \, k_{1}^{6} - k_{1}^{5} k_{2} - 3 \, k_{1}^{4} k_{2}^{2} + 2 \, k_{1}^{3} k_{2}^{3} - 3 \, k_{1}^{2} k_{2}^{4} - k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left(2 \, {\left(k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(3 \, k_{1}^{6} + 7 \, k_{1}^{5} k_{2} + k_{1}^{4} k_{2}^{2} - 6 \, k_{1}^{3} k_{2}^{3} + k_{1}^{2} k_{2}^{4} + 7 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + 3 \, {\left({\left(k_{1}^{6} - 2 \, k_{1}^{5} k_{2} - k_{1}^{4} k_{2}^{2} + 4 \, k_{1}^{3} k_{2}^{3} - k_{1}^{2} k_{2}^{4} - 2 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left({\left(2 \, k_{1} + 3 \, k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{6} + 2 \, k_{1}^{5} k_{2} - k_{1}^{4} k_{2}^{2} - 4 \, k_{1}^{3} k_{2}^{3} - k_{1}^{2} k_{2}^{4} + 2 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left({\left(k_{1} + 3 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(3 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left({\left(3 \, k_{1}^{6} + 8 \, k_{1}^{5} k_{2} + 5 \, k_{1}^{4} k_{2}^{2} + 5 \, k_{1}^{2} k_{2}^{4} + 8 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(k_{1} + k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(3 \, k_{1}^{6} + 4 \, k_{1}^{5} k_{2} - 11 \, k_{1}^{4} k_{2}^{2} - 24 \, k_{1}^{3} k_{2}^{3} - 11 \, k_{1}^{2} k_{2}^{4} + 4 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(2 \, k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(\beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} D[0]\left(\alpha\right)\left(x, t_{1}, t_{2}, t_{3}\right)\right)} D[0, 0]\left(\alpha\right)\left(x, t_{1}, t_{2}, t_{3}\right) + 3 \, {\left(2 \, {\left({\left({\left(3 \, k_{1}^{6} + 4 \, k_{1}^{5} k_{2} - 11 \, k_{1}^{4} k_{2}^{2} - 24 \, k_{1}^{3} k_{2}^{3} - 11 \, k_{1}^{2} k_{2}^{4} + 4 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(3 \, k_{1}^{6} + 8 \, k_{1}^{5} k_{2} - 3 \, k_{1}^{4} k_{2}^{2} - 16 \, k_{1}^{3} k_{2}^{3} - 3 \, k_{1}^{2} k_{2}^{4} + 8 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left(2 \, {\left(k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left({\left(3 \, k_{1}^{6} + 8 \, k_{1}^{5} k_{2} + 5 \, k_{1}^{4} k_{2}^{2} + 5 \, k_{1}^{2} k_{2}^{4} + 8 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(k_{1} + k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(3 \, k_{1}^{6} + 16 \, k_{1}^{5} k_{2} + 37 \, k_{1}^{4} k_{2}^{2} + 48 \, k_{1}^{3} k_{2}^{3} + 37 \, k_{1}^{2} k_{2}^{4} + 16 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(2 \, k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(\beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} D[0]\left(\alpha\right)\left(x, t_{1}, t_{2}, t_{3}\right)^{2} + 2 \, {\left({\left(3 \, {\left(k_{1}^{6} - 2 \, k_{1}^{5} k_{2} - k_{1}^{4} k_{2}^{2} + 4 \, k_{1}^{3} k_{2}^{3} - k_{1}^{2} k_{2}^{4} - 2 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left({\left(3 \, k_{1} + 2 \, k_{2}\right)} x + 3 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + 2 \, {\left(3 \, k_{1}^{6} - k_{1}^{5} k_{2} - 3 \, k_{1}^{4} k_{2}^{2} + 2 \, k_{1}^{3} k_{2}^{3} - 3 \, k_{1}^{2} k_{2}^{4} - k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left(2 \, {\left(k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(3 \, k_{1}^{6} + 4 \, k_{1}^{5} k_{2} - 11 \, k_{1}^{4} k_{2}^{2} - 24 \, k_{1}^{3} k_{2}^{3} - 11 \, k_{1}^{2} k_{2}^{4} + 4 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left({\left(3 \, k_{1}^{6} + 8 \, k_{1}^{5} k_{2} + 5 \, k_{1}^{4} k_{2}^{2} + 5 \, k_{1}^{2} k_{2}^{4} + 8 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(k_{1} + k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + 3 \, {\left(k_{1}^{6} + 2 \, k_{1}^{5} k_{2} - k_{1}^{4} k_{2}^{2} - 4 \, k_{1}^{3} k_{2}^{3} - k_{1}^{2} k_{2}^{4} + 2 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left({\left(3 \, k_{1} + k_{2}\right)} x + 3 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + 2 \, {\left(3 \, k_{1}^{6} + 7 \, k_{1}^{5} k_{2} + k_{1}^{4} k_{2}^{2} - 6 \, k_{1}^{3} k_{2}^{3} + k_{1}^{2} k_{2}^{4} + 7 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(2 \, k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(\beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} D[0, 0]\left(\alpha\right)\left(x, t_{1}, t_{2}, t_{3}\right) + 4 \, {\left({\left({\left(3 \, k_{1}^{7} + 8 \, k_{1}^{6} k_{2} - 5 \, k_{1}^{5} k_{2}^{2} - 40 \, k_{1}^{4} k_{2}^{3} - 55 \, k_{1}^{3} k_{2}^{4} - 32 \, k_{1}^{2} k_{2}^{5} - 7 \, k_{1} k_{2}^{6}\right)} e^{\left({\left(k_{1} + k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(3 \, k_{1}^{7} + 16 \, k_{1}^{6} k_{2} + 27 \, k_{1}^{5} k_{2}^{2} + 8 \, k_{1}^{4} k_{2}^{3} - 23 \, k_{1}^{3} k_{2}^{4} - 24 \, k_{1}^{2} k_{2}^{5} - 7 \, k_{1} k_{2}^{6}\right)} e^{\left({\left(2 \, k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(\beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left({\left(3 \, k_{1}^{7} + 4 \, k_{1}^{6} k_{2} - 9 \, k_{1}^{5} k_{2}^{2} - 16 \, k_{1}^{4} k_{2}^{3} + k_{1}^{3} k_{2}^{4} + 12 \, k_{1}^{2} k_{2}^{5} + 5 \, k_{1} k_{2}^{6}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(3 \, k_{1}^{7} + 8 \, k_{1}^{6} k_{2} - k_{1}^{5} k_{2}^{2} - 16 \, k_{1}^{4} k_{2}^{3} - 7 \, k_{1}^{3} k_{2}^{4} + 8 \, k_{1}^{2} k_{2}^{5} + 5 \, k_{1} k_{2}^{6}\right)} e^{\left(2 \, {\left(k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} D[0]\left(\alpha\right)\left(x, t_{1}, t_{2}, t_{3}\right) + {\left(5 \, {\left(k_{1}^{6} k_{2}^{2} + 2 \, k_{1}^{5} k_{2}^{3} - k_{1}^{4} k_{2}^{4} - 4 \, k_{1}^{3} k_{2}^{5} - k_{1}^{2} k_{2}^{6} + 2 \, k_{1} k_{2}^{7} + k_{2}^{8}\right)} e^{\left({\left(3 \, k_{1} + k_{2}\right)} x + 3 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + 5 \, {\left(k_{1}^{6} k_{2}^{2} + 6 \, k_{1}^{5} k_{2}^{3} + 15 \, k_{1}^{4} k_{2}^{4} + 20 \, k_{1}^{3} k_{2}^{5} + 15 \, k_{1}^{2} k_{2}^{6} + 6 \, k_{1} k_{2}^{7} + k_{2}^{8}\right)} e^{\left(k_{2} x\right)} + {\left(6 \, k_{1}^{8} + 16 \, k_{1}^{7} k_{2} - 15 \, k_{1}^{6} k_{2}^{2} - 90 \, k_{1}^{5} k_{2}^{3} - 85 \, k_{1}^{4} k_{2}^{4} + 36 \, k_{1}^{3} k_{2}^{5} + 111 \, k_{1}^{2} k_{2}^{6} + 70 \, k_{1} k_{2}^{7} + 15 \, k_{2}^{8}\right)} e^{\left({\left(k_{1} + k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(6 \, k_{1}^{8} + 32 \, k_{1}^{7} k_{2} + 49 \, k_{1}^{6} k_{2}^{2} - 14 \, k_{1}^{5} k_{2}^{3} - 101 \, k_{1}^{4} k_{2}^{4} - 68 \, k_{1}^{3} k_{2}^{5} + 31 \, k_{1}^{2} k_{2}^{6} + 50 \, k_{1} k_{2}^{7} + 15 \, k_{2}^{8}\right)} e^{\left({\left(2 \, k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(\beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left({\left(k_{1}^{6} k_{2}^{2} - 2 \, k_{1}^{5} k_{2}^{3} - k_{1}^{4} k_{2}^{4} + 4 \, k_{1}^{3} k_{2}^{5} - k_{1}^{2} k_{2}^{6} - 2 \, k_{1} k_{2}^{7} + k_{2}^{8}\right)} e^{\left({\left(3 \, k_{1} + 2 \, k_{2}\right)} x + 3 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{6} k_{2}^{2} + 6 \, k_{1}^{5} k_{2}^{3} + 15 \, k_{1}^{4} k_{2}^{4} + 20 \, k_{1}^{3} k_{2}^{5} + 15 \, k_{1}^{2} k_{2}^{6} + 6 \, k_{1} k_{2}^{7} + k_{2}^{8}\right)} e^{\left(2 \, k_{2} x\right)} - {\left(6 \, k_{1}^{8} + 8 \, k_{1}^{7} k_{2} - 17 \, k_{1}^{6} k_{2}^{2} - 26 \, k_{1}^{5} k_{2}^{3} + 13 \, k_{1}^{4} k_{2}^{4} + 28 \, k_{1}^{3} k_{2}^{5} + k_{1}^{2} k_{2}^{6} - 10 \, k_{1} k_{2}^{7} - 3 \, k_{2}^{8}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(6 \, k_{1}^{8} + 16 \, k_{1}^{7} k_{2} - k_{1}^{6} k_{2}^{2} - 34 \, k_{1}^{5} k_{2}^{3} - 19 \, k_{1}^{4} k_{2}^{4} + 20 \, k_{1}^{3} k_{2}^{5} + 17 \, k_{1}^{2} k_{2}^{6} - 2 \, k_{1} k_{2}^{7} - 3 \, k_{2}^{8}\right)} e^{\left(2 \, {\left(k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} D[0]\left(\beta\right)\left(x, t_{1}, t_{2}, t_{3}\right)\right)} D[0, 0]\left(\beta\right)\left(x, t_{1}, t_{2}, t_{3}\right)

WARNING: Output truncated!  
full_output.txt



\newcommand{\Bold}[1]{\mathbf{#1}}2 \, {\left({\left({\left(k_{1}^{6} + 2 \, k_{1}^{5} k_{2} - k_{1}^{4} k_{2}^{2} - 4 \, k_{1}^{3} k_{2}^{3} - k_{1}^{2} k_{2}^{4} + 2 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left({\left(3 \, k_{1} + k_{2}\right)} x + 3 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{6} + 6 \, k_{1}^{5} k_{2} + 15 \, k_{1}^{4} k_{2}^{2} + 20 \, k_{1}^{3} k_{2}^{3} + 15 \, k_{1}^{2} k_{2}^{4} + 6 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left(k_{2} x\right)} + {\left(3 \, k_{1}^{6} + 10 \, k_{1}^{5} k_{2} + 13 \, k_{1}^{4} k_{2}^{2} + 12 \, k_{1}^{3} k_{2}^{3} + 13 \, k_{1}^{2} k_{2}^{4} + 10 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(2 \, k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(3 \, k_{1}^{6} + 14 \, k_{1}^{5} k_{2} + 29 \, k_{1}^{4} k_{2}^{2} + 36 \, k_{1}^{3} k_{2}^{3} + 29 \, k_{1}^{2} k_{2}^{4} + 14 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(k_{1} + k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(\beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left({\left(k_{1}^{6} - 2 \, k_{1}^{5} k_{2} - k_{1}^{4} k_{2}^{2} + 4 \, k_{1}^{3} k_{2}^{3} - k_{1}^{2} k_{2}^{4} - 2 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left({\left(3 \, k_{1} + 2 \, k_{2}\right)} x + 3 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{6} + 6 \, k_{1}^{5} k_{2} + 15 \, k_{1}^{4} k_{2}^{2} + 20 \, k_{1}^{3} k_{2}^{3} + 15 \, k_{1}^{2} k_{2}^{4} + 6 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left(2 \, k_{2} x\right)} + {\left(3 \, k_{1}^{6} + 2 \, k_{1}^{5} k_{2} - 3 \, k_{1}^{4} k_{2}^{2} - 4 \, k_{1}^{3} k_{2}^{3} - 3 \, k_{1}^{2} k_{2}^{4} + 2 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left(2 \, {\left(k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(3 \, k_{1}^{6} + 10 \, k_{1}^{5} k_{2} + 13 \, k_{1}^{4} k_{2}^{2} + 12 \, k_{1}^{3} k_{2}^{3} + 13 \, k_{1}^{2} k_{2}^{4} + 10 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} D[0]\left(\beta\right)\left(x, t_{1}, t_{2}, t_{3}\right)^{5} - 2 \, {\left({\left({\left(3 \, k_{1}^{6} + 10 \, k_{1}^{5} k_{2} + 13 \, k_{1}^{4} k_{2}^{2} + 12 \, k_{1}^{3} k_{2}^{3} + 13 \, k_{1}^{2} k_{2}^{4} + 10 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(2 \, k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(3 \, k_{1}^{6} + 14 \, k_{1}^{5} k_{2} + 29 \, k_{1}^{4} k_{2}^{2} + 36 \, k_{1}^{3} k_{2}^{3} + 29 \, k_{1}^{2} k_{2}^{4} + 14 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(k_{1} + k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(\beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left({\left(3 \, k_{1}^{6} + 2 \, k_{1}^{5} k_{2} - 3 \, k_{1}^{4} k_{2}^{2} - 4 \, k_{1}^{3} k_{2}^{3} - 3 \, k_{1}^{2} k_{2}^{4} + 2 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left(2 \, {\left(k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(3 \, k_{1}^{6} + 10 \, k_{1}^{5} k_{2} + 13 \, k_{1}^{4} k_{2}^{2} + 12 \, k_{1}^{3} k_{2}^{3} + 13 \, k_{1}^{2} k_{2}^{4} + 10 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left({\left(k_{1}^{6} - 2 \, k_{1}^{5} k_{2} - k_{1}^{4} k_{2}^{2} + 4 \, k_{1}^{3} k_{2}^{3} - k_{1}^{2} k_{2}^{4} - 2 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left({\left(2 \, k_{1} + 3 \, k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(k_{1}^{6} + 2 \, k_{1}^{5} k_{2} - k_{1}^{4} k_{2}^{2} - 4 \, k_{1}^{3} k_{2}^{3} - k_{1}^{2} k_{2}^{4} + 2 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left({\left(k_{1} + 3 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(3 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(k_{1}^{6} + 6 \, k_{1}^{5} k_{2} + 15 \, k_{1}^{4} k_{2}^{2} + 20 \, k_{1}^{3} k_{2}^{3} + 15 \, k_{1}^{2} k_{2}^{4} + 6 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left(k_{1} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{6} + 6 \, k_{1}^{5} k_{2} + 15 \, k_{1}^{4} k_{2}^{2} + 20 \, k_{1}^{3} k_{2}^{3} + 15 \, k_{1}^{2} k_{2}^{4} + 6 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left(2 \, k_{1} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} D[0]\left(\alpha\right)\left(x, t_{1}, t_{2}, t_{3}\right)^{5} - 10 \, {\left(4 \, {\left({\left({\left(k_{1}^{5} k_{2} + 4 \, k_{1}^{4} k_{2}^{2} + 6 \, k_{1}^{3} k_{2}^{3} + 4 \, k_{1}^{2} k_{2}^{4} + k_{1} k_{2}^{5}\right)} e^{\left({\left(2 \, k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{5} k_{2} + 4 \, k_{1}^{4} k_{2}^{2} + 6 \, k_{1}^{3} k_{2}^{3} + 4 \, k_{1}^{2} k_{2}^{4} + k_{1} k_{2}^{5}\right)} e^{\left({\left(k_{1} + k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(\beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left({\left(k_{1}^{5} k_{2} - 2 \, k_{1}^{3} k_{2}^{3} + k_{1} k_{2}^{5}\right)} e^{\left(2 \, {\left(k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{5} k_{2} + 4 \, k_{1}^{4} k_{2}^{2} + 6 \, k_{1}^{3} k_{2}^{3} + 4 \, k_{1}^{2} k_{2}^{4} + k_{1} k_{2}^{5}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} D[0]\left(\alpha\right)\left(x, t_{1}, t_{2}, t_{3}\right) + {\left({\left(k_{1}^{6} k_{2} + 2 \, k_{1}^{5} k_{2}^{2} - 5 \, k_{1}^{4} k_{2}^{3} - 20 \, k_{1}^{3} k_{2}^{4} - 25 \, k_{1}^{2} k_{2}^{5} - 14 \, k_{1} k_{2}^{6} - 3 \, k_{2}^{7}\right)} e^{\left({\left(k_{1} + k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(k_{1}^{6} k_{2} + 2 \, k_{1}^{5} k_{2}^{2} - k_{1}^{4} k_{2}^{3} - 4 \, k_{1}^{3} k_{2}^{4} - k_{1}^{2} k_{2}^{5} + 2 \, k_{1} k_{2}^{6} + k_{2}^{7}\right)} e^{\left({\left(3 \, k_{1} + k_{2}\right)} x + 3 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{6} k_{2} + 6 \, k_{1}^{5} k_{2}^{2} + 11 \, k_{1}^{4} k_{2}^{3} + 4 \, k_{1}^{3} k_{2}^{4} - 9 \, k_{1}^{2} k_{2}^{5} - 10 \, k_{1} k_{2}^{6} - 3 \, k_{2}^{7}\right)} e^{\left({\left(2 \, k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(k_{1}^{6} k_{2} + 6 \, k_{1}^{5} k_{2}^{2} + 15 \, k_{1}^{4} k_{2}^{3} + 20 \, k_{1}^{3} k_{2}^{4} + 15 \, k_{1}^{2} k_{2}^{5} + 6 \, k_{1} k_{2}^{6} + k_{2}^{7}\right)} e^{\left(k_{2} x\right)}\right)} e^{\left(\beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left({\left(k_{1}^{6} k_{2} - 2 \, k_{1}^{5} k_{2}^{2} - 5 \, k_{1}^{4} k_{2}^{3} + 4 \, k_{1}^{3} k_{2}^{4} + 7 \, k_{1}^{2} k_{2}^{5} - 2 \, k_{1} k_{2}^{6} - 3 \, k_{2}^{7}\right)} e^{\left(2 \, {\left(k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(k_{1}^{6} k_{2} - 2 \, k_{1}^{5} k_{2}^{2} - k_{1}^{4} k_{2}^{3} + 4 \, k_{1}^{3} k_{2}^{4} - k_{1}^{2} k_{2}^{5} - 2 \, k_{1} k_{2}^{6} + k_{2}^{7}\right)} e^{\left({\left(3 \, k_{1} + 2 \, k_{2}\right)} x + 3 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{6} k_{2} + 6 \, k_{1}^{5} k_{2}^{2} + 11 \, k_{1}^{4} k_{2}^{3} + 4 \, k_{1}^{3} k_{2}^{4} - 9 \, k_{1}^{2} k_{2}^{5} - 10 \, k_{1} k_{2}^{6} - 3 \, k_{2}^{7}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(k_{1}^{6} k_{2} + 6 \, k_{1}^{5} k_{2}^{2} + 15 \, k_{1}^{4} k_{2}^{3} + 20 \, k_{1}^{3} k_{2}^{4} + 15 \, k_{1}^{2} k_{2}^{5} + 6 \, k_{1} k_{2}^{6} + k_{2}^{7}\right)} e^{\left(2 \, k_{2} x\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} D[0]\left(\beta\right)\left(x, t_{1}, t_{2}, t_{3}\right)^{4} - 10 \, {\left({\left({\left(3 \, k_{1}^{7} + 10 \, k_{1}^{6} k_{2} + 9 \, k_{1}^{5} k_{2}^{2} - 4 \, k_{1}^{4} k_{2}^{3} - 11 \, k_{1}^{3} k_{2}^{4} - 6 \, k_{1}^{2} k_{2}^{5} - k_{1} k_{2}^{6}\right)} e^{\left({\left(2 \, k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(3 \, k_{1}^{7} + 14 \, k_{1}^{6} k_{2} + 25 \, k_{1}^{5} k_{2}^{2} + 20 \, k_{1}^{4} k_{2}^{3} + 5 \, k_{1}^{3} k_{2}^{4} - 2 \, k_{1}^{2} k_{2}^{5} - k_{1} k_{2}^{6}\right)} e^{\left({\left(k_{1} + k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(\beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left({\left(3 \, k_{1}^{7} + 2 \, k_{1}^{6} k_{2} - 7 \, k_{1}^{5} k_{2}^{2} - 4 \, k_{1}^{4} k_{2}^{3} + 5 \, k_{1}^{3} k_{2}^{4} + 2 \, k_{1}^{2} k_{2}^{5} - k_{1} k_{2}^{6}\right)} e^{\left(2 \, {\left(k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(3 \, k_{1}^{7} + 10 \, k_{1}^{6} k_{2} + 9 \, k_{1}^{5} k_{2}^{2} - 4 \, k_{1}^{4} k_{2}^{3} - 11 \, k_{1}^{3} k_{2}^{4} - 6 \, k_{1}^{2} k_{2}^{5} - k_{1} k_{2}^{6}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left({\left(k_{1}^{7} - 2 \, k_{1}^{6} k_{2} - k_{1}^{5} k_{2}^{2} + 4 \, k_{1}^{4} k_{2}^{3} - k_{1}^{3} k_{2}^{4} - 2 \, k_{1}^{2} k_{2}^{5} + k_{1} k_{2}^{6}\right)} e^{\left({\left(2 \, k_{1} + 3 \, k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(k_{1}^{7} + 2 \, k_{1}^{6} k_{2} - k_{1}^{5} k_{2}^{2} - 4 \, k_{1}^{4} k_{2}^{3} - k_{1}^{3} k_{2}^{4} + 2 \, k_{1}^{2} k_{2}^{5} + k_{1} k_{2}^{6}\right)} e^{\left({\left(k_{1} + 3 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(3 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(k_{1}^{7} + 6 \, k_{1}^{6} k_{2} + 15 \, k_{1}^{5} k_{2}^{2} + 20 \, k_{1}^{4} k_{2}^{3} + 15 \, k_{1}^{3} k_{2}^{4} + 6 \, k_{1}^{2} k_{2}^{5} + k_{1} k_{2}^{6}\right)} e^{\left(k_{1} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{7} + 6 \, k_{1}^{6} k_{2} + 15 \, k_{1}^{5} k_{2}^{2} + 20 \, k_{1}^{4} k_{2}^{3} + 15 \, k_{1}^{3} k_{2}^{4} + 6 \, k_{1}^{2} k_{2}^{5} + k_{1} k_{2}^{6}\right)} e^{\left(2 \, k_{1} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} D[0]\left(\alpha\right)\left(x, t_{1}, t_{2}, t_{3}\right)^{4} - 4 \, {\left({\left({\left(15 \, k_{1}^{8} + 50 \, k_{1}^{7} k_{2} + 31 \, k_{1}^{6} k_{2}^{2} - 68 \, k_{1}^{5} k_{2}^{3} - 101 \, k_{1}^{4} k_{2}^{4} - 14 \, k_{1}^{3} k_{2}^{5} + 49 \, k_{1}^{2} k_{2}^{6} + 32 \, k_{1} k_{2}^{7} + 6 \, k_{2}^{8}\right)} e^{\left({\left(2 \, k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(15 \, k_{1}^{8} + 70 \, k_{1}^{7} k_{2} + 111 \, k_{1}^{6} k_{2}^{2} + 36 \, k_{1}^{5} k_{2}^{3} - 85 \, k_{1}^{4} k_{2}^{4} - 90 \, k_{1}^{3} k_{2}^{5} - 15 \, k_{1}^{2} k_{2}^{6} + 16 \, k_{1} k_{2}^{7} + 6 \, k_{2}^{8}\right)} e^{\left({\left(k_{1} + k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(\beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left({\left(15 \, k_{1}^{8} + 10 \, k_{1}^{7} k_{2} - 49 \, k_{1}^{6} k_{2}^{2} - 28 \, k_{1}^{5} k_{2}^{3} + 59 \, k_{1}^{4} k_{2}^{4} + 26 \, k_{1}^{3} k_{2}^{5} - 31 \, k_{1}^{2} k_{2}^{6} - 8 \, k_{1} k_{2}^{7} + 6 \, k_{2}^{8}\right)} e^{\left(2 \, {\left(k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(15 \, k_{1}^{8} + 50 \, k_{1}^{7} k_{2} + 31 \, k_{1}^{6} k_{2}^{2} - 68 \, k_{1}^{5} k_{2}^{3} - 101 \, k_{1}^{4} k_{2}^{4} - 14 \, k_{1}^{3} k_{2}^{5} + 49 \, k_{1}^{2} k_{2}^{6} + 32 \, k_{1} k_{2}^{7} + 6 \, k_{2}^{8}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + 5 \, {\left({\left(k_{1}^{8} - 2 \, k_{1}^{7} k_{2} - k_{1}^{6} k_{2}^{2} + 4 \, k_{1}^{5} k_{2}^{3} - k_{1}^{4} k_{2}^{4} - 2 \, k_{1}^{3} k_{2}^{5} + k_{1}^{2} k_{2}^{6}\right)} e^{\left({\left(2 \, k_{1} + 3 \, k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(k_{1}^{8} + 2 \, k_{1}^{7} k_{2} - k_{1}^{6} k_{2}^{2} - 4 \, k_{1}^{5} k_{2}^{3} - k_{1}^{4} k_{2}^{4} + 2 \, k_{1}^{3} k_{2}^{5} + k_{1}^{2} k_{2}^{6}\right)} e^{\left({\left(k_{1} + 3 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(3 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - 5 \, {\left(k_{1}^{8} + 6 \, k_{1}^{7} k_{2} + 15 \, k_{1}^{6} k_{2}^{2} + 20 \, k_{1}^{5} k_{2}^{3} + 15 \, k_{1}^{4} k_{2}^{4} + 6 \, k_{1}^{3} k_{2}^{5} + k_{1}^{2} k_{2}^{6}\right)} e^{\left(k_{1} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + 5 \, {\left(k_{1}^{8} + 6 \, k_{1}^{7} k_{2} + 15 \, k_{1}^{6} k_{2}^{2} + 20 \, k_{1}^{5} k_{2}^{3} + 15 \, k_{1}^{4} k_{2}^{4} + 6 \, k_{1}^{3} k_{2}^{5} + k_{1}^{2} k_{2}^{6}\right)} e^{\left(2 \, k_{1} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} D[0]\left(\alpha\right)\left(x, t_{1}, t_{2}, t_{3}\right)^{3} - 4 \, {\left(2 \, {\left({\left({\left(3 \, k_{1}^{6} - 4 \, k_{1}^{5} k_{2} - 3 \, k_{1}^{4} k_{2}^{2} + 8 \, k_{1}^{3} k_{2}^{3} - 3 \, k_{1}^{2} k_{2}^{4} - 4 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left(2 \, {\left(k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(3 \, k_{1}^{6} + 16 \, k_{1}^{5} k_{2} + 37 \, k_{1}^{4} k_{2}^{2} + 48 \, k_{1}^{3} k_{2}^{3} + 37 \, k_{1}^{2} k_{2}^{4} + 16 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left({\left(3 \, k_{1}^{6} + 8 \, k_{1}^{5} k_{2} + 5 \, k_{1}^{4} k_{2}^{2} + 5 \, k_{1}^{2} k_{2}^{4} + 8 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(k_{1} + k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(3 \, k_{1}^{6} + 16 \, k_{1}^{5} k_{2} + 37 \, k_{1}^{4} k_{2}^{2} + 48 \, k_{1}^{3} k_{2}^{3} + 37 \, k_{1}^{2} k_{2}^{4} + 16 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(2 \, k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(\beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} D[0]\left(\alpha\right)\left(x, t_{1}, t_{2}, t_{3}\right)^{2} + 2 \, {\left({\left(3 \, {\left(k_{1}^{6} - 2 \, k_{1}^{5} k_{2} - k_{1}^{4} k_{2}^{2} + 4 \, k_{1}^{3} k_{2}^{3} - k_{1}^{2} k_{2}^{4} - 2 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left({\left(3 \, k_{1} + 2 \, k_{2}\right)} x + 3 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + 2 \, {\left(3 \, k_{1}^{6} + 5 \, k_{1}^{5} k_{2} - 3 \, k_{1}^{4} k_{2}^{2} - 10 \, k_{1}^{3} k_{2}^{3} - 3 \, k_{1}^{2} k_{2}^{4} + 5 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left(2 \, {\left(k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(3 \, k_{1}^{6} + 16 \, k_{1}^{5} k_{2} + 37 \, k_{1}^{4} k_{2}^{2} + 48 \, k_{1}^{3} k_{2}^{3} + 37 \, k_{1}^{2} k_{2}^{4} + 16 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left({\left(3 \, k_{1}^{6} + 8 \, k_{1}^{5} k_{2} + 5 \, k_{1}^{4} k_{2}^{2} + 5 \, k_{1}^{2} k_{2}^{4} + 8 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(k_{1} + k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + 3 \, {\left(k_{1}^{6} + 2 \, k_{1}^{5} k_{2} - k_{1}^{4} k_{2}^{2} - 4 \, k_{1}^{3} k_{2}^{3} - k_{1}^{2} k_{2}^{4} + 2 \, k_{1} k_{2}^{5} + 

...

, t_{2}, t_{3}\right)\right)} - {\left(3 \, k_{1}^{8} + 10 \, k_{1}^{7} k_{2} + 5 \, k_{1}^{6} k_{2}^{2} - 16 \, k_{1}^{5} k_{2}^{3} - 19 \, k_{1}^{4} k_{2}^{4} + 2 \, k_{1}^{3} k_{2}^{5} + 11 \, k_{1}^{2} k_{2}^{6} + 4 \, k_{1} k_{2}^{7}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left({\left(3 \, k_{1}^{8} + 14 \, k_{1}^{7} k_{2} + 21 \, k_{1}^{6} k_{2}^{2} - 35 \, k_{1}^{4} k_{2}^{4} - 42 \, k_{1}^{3} k_{2}^{5} - 21 \, k_{1}^{2} k_{2}^{6} - 4 \, k_{1} k_{2}^{7}\right)} e^{\left({\left(k_{1} + k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(3 \, k_{1}^{8} + 10 \, k_{1}^{7} k_{2} + 5 \, k_{1}^{6} k_{2}^{2} - 16 \, k_{1}^{5} k_{2}^{3} - 19 \, k_{1}^{4} k_{2}^{4} + 2 \, k_{1}^{3} k_{2}^{5} + 11 \, k_{1}^{2} k_{2}^{6} + 4 \, k_{1} k_{2}^{7}\right)} e^{\left({\left(2 \, k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(\beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + 3 \, {\left({\left(k_{1}^{8} - 2 \, k_{1}^{7} k_{2} - k_{1}^{6} k_{2}^{2} + 4 \, k_{1}^{5} k_{2}^{3} - k_{1}^{4} k_{2}^{4} - 2 \, k_{1}^{3} k_{2}^{5} + k_{1}^{2} k_{2}^{6}\right)} e^{\left({\left(2 \, k_{1} + 3 \, k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(k_{1}^{8} + 2 \, k_{1}^{7} k_{2} - k_{1}^{6} k_{2}^{2} - 4 \, k_{1}^{5} k_{2}^{3} - k_{1}^{4} k_{2}^{4} + 2 \, k_{1}^{3} k_{2}^{5} + k_{1}^{2} k_{2}^{6}\right)} e^{\left({\left(k_{1} + 3 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(3 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} D[0]\left(\alpha\right)\left(x, t_{1}, t_{2}, t_{3}\right) + {\left(5 \, {\left(k_{1}^{6} k_{2}^{3} + 2 \, k_{1}^{5} k_{2}^{4} - k_{1}^{4} k_{2}^{5} - 4 \, k_{1}^{3} k_{2}^{6} - k_{1}^{2} k_{2}^{7} + 2 \, k_{1} k_{2}^{8} + k_{2}^{9}\right)} e^{\left({\left(3 \, k_{1} + k_{2}\right)} x + 3 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + 5 \, {\left(k_{1}^{6} k_{2}^{3} + 6 \, k_{1}^{5} k_{2}^{4} + 15 \, k_{1}^{4} k_{2}^{5} + 20 \, k_{1}^{3} k_{2}^{6} + 15 \, k_{1}^{2} k_{2}^{7} + 6 \, k_{1} k_{2}^{8} + k_{2}^{9}\right)} e^{\left(k_{2} x\right)} - {\left(6 \, k_{1}^{9} + 14 \, k_{1}^{8} k_{2} - 22 \, k_{1}^{7} k_{2}^{2} - 81 \, k_{1}^{6} k_{2}^{3} - 24 \, k_{1}^{5} k_{2}^{4} + 105 \, k_{1}^{4} k_{2}^{5} + 90 \, k_{1}^{3} k_{2}^{6} - 23 \, k_{1}^{2} k_{2}^{7} - 50 \, k_{1} k_{2}^{8} - 15 \, k_{2}^{9}\right)} e^{\left({\left(2 \, k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(6 \, k_{1}^{9} + 34 \, k_{1}^{8} k_{2} + 58 \, k_{1}^{7} k_{2}^{2} - 15 \, k_{1}^{6} k_{2}^{3} - 160 \, k_{1}^{5} k_{2}^{4} - 169 \, k_{1}^{4} k_{2}^{5} - 6 \, k_{1}^{3} k_{2}^{6} + 103 \, k_{1}^{2} k_{2}^{7} + 70 \, k_{1} k_{2}^{8} + 15 \, k_{2}^{9}\right)} e^{\left({\left(k_{1} + k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(\beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left({\left(k_{1}^{6} k_{2}^{3} - 2 \, k_{1}^{5} k_{2}^{4} - k_{1}^{4} k_{2}^{5} + 4 \, k_{1}^{3} k_{2}^{6} - k_{1}^{2} k_{2}^{7} - 2 \, k_{1} k_{2}^{8} + k_{2}^{9}\right)} e^{\left({\left(3 \, k_{1} + 2 \, k_{2}\right)} x + 3 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{6} k_{2}^{3} + 6 \, k_{1}^{5} k_{2}^{4} + 15 \, k_{1}^{4} k_{2}^{5} + 20 \, k_{1}^{3} k_{2}^{6} + 15 \, k_{1}^{2} k_{2}^{7} + 6 \, k_{1} k_{2}^{8} + k_{2}^{9}\right)} e^{\left(2 \, k_{2} x\right)} + {\left(12 \, k_{1}^{9} + 2 \, k_{1}^{8} k_{2} - 60 \, k_{1}^{7} k_{2}^{2} - 31 \, k_{1}^{6} k_{2}^{3} + 86 \, k_{1}^{5} k_{2}^{4} + 59 \, k_{1}^{4} k_{2}^{5} - 40 \, k_{1}^{3} k_{2}^{6} - 33 \, k_{1}^{2} k_{2}^{7} + 2 \, k_{1} k_{2}^{8} + 3 \, k_{2}^{9}\right)} e^{\left(2 \, {\left(k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(12 \, k_{1}^{9} + 46 \, k_{1}^{8} k_{2} + 28 \, k_{1}^{7} k_{2}^{2} - 81 \, k_{1}^{6} k_{2}^{3} - 102 \, k_{1}^{5} k_{2}^{4} + 21 \, k_{1}^{4} k_{2}^{5} + 72 \, k_{1}^{3} k_{2}^{6} + 17 \, k_{1}^{2} k_{2}^{7} - 10 \, k_{1} k_{2}^{8} - 3 \, k_{2}^{9}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + 6 \, {\left(3 \, {\left({\left(k_{1}^{7} - 2 \, k_{1}^{6} k_{2} - k_{1}^{5} k_{2}^{2} + 4 \, k_{1}^{4} k_{2}^{3} - k_{1}^{3} k_{2}^{4} - 2 \, k_{1}^{2} k_{2}^{5} + k_{1} k_{2}^{6}\right)} e^{\left({\left(2 \, k_{1} + 3 \, k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{7} + 2 \, k_{1}^{6} k_{2} - k_{1}^{5} k_{2}^{2} - 4 \, k_{1}^{4} k_{2}^{3} - k_{1}^{3} k_{2}^{4} + 2 \, k_{1}^{2} k_{2}^{5} + k_{1} k_{2}^{6}\right)} e^{\left({\left(k_{1} + 3 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(3 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(3 \, {\left(k_{1}^{6} k_{2} + 2 \, k_{1}^{5} k_{2}^{2} - k_{1}^{4} k_{2}^{3} - 4 \, k_{1}^{3} k_{2}^{4} - k_{1}^{2} k_{2}^{5} + 2 \, k_{1} k_{2}^{6} + k_{2}^{7}\right)} e^{\left({\left(3 \, k_{1} + k_{2}\right)} x + 3 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(3 \, k_{1}^{7} + 10 \, k_{1}^{6} k_{2} + 3 \, k_{1}^{5} k_{2}^{2} - 22 \, k_{1}^{4} k_{2}^{3} - 23 \, k_{1}^{3} k_{2}^{4} + 6 \, k_{1}^{2} k_{2}^{5} + 17 \, k_{1} k_{2}^{6} + 6 \, k_{2}^{7}\right)} e^{\left({\left(2 \, k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(3 \, k_{1}^{7} + 11 \, k_{1}^{6} k_{2} + 13 \, k_{1}^{5} k_{2}^{2} + 5 \, k_{1}^{4} k_{2}^{3} + 5 \, k_{1}^{3} k_{2}^{4} + 13 \, k_{1}^{2} k_{2}^{5} + 11 \, k_{1} k_{2}^{6} + 3 \, k_{2}^{7}\right)} e^{\left({\left(k_{1} + k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(\beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(3 \, {\left(k_{1}^{6} k_{2} - 2 \, k_{1}^{5} k_{2}^{2} - k_{1}^{4} k_{2}^{3} + 4 \, k_{1}^{3} k_{2}^{4} - k_{1}^{2} k_{2}^{5} - 2 \, k_{1} k_{2}^{6} + k_{2}^{7}\right)} e^{\left({\left(3 \, k_{1} + 2 \, k_{2}\right)} x + 3 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + 2 \, {\left(3 \, k_{1}^{7} + 2 \, k_{1}^{6} k_{2} - 4 \, k_{1}^{5} k_{2}^{2} - k_{1}^{4} k_{2}^{3} - k_{1}^{3} k_{2}^{4} - 4 \, k_{1}^{2} k_{2}^{5} + 2 \, k_{1} k_{2}^{6} + 3 \, k_{2}^{7}\right)} e^{\left(2 \, {\left(k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(6 \, k_{1}^{7} + 17 \, k_{1}^{6} k_{2} + 6 \, k_{1}^{5} k_{2}^{2} - 23 \, k_{1}^{4} k_{2}^{3} - 22 \, k_{1}^{3} k_{2}^{4} + 3 \, k_{1}^{2} k_{2}^{5} + 10 \, k_{1} k_{2}^{6} + 3 \, k_{2}^{7}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(2 \, {\left({\left(3 \, k_{1}^{6} - k_{1}^{5} k_{2} - 3 \, k_{1}^{4} k_{2}^{2} + 2 \, k_{1}^{3} k_{2}^{3} - 3 \, k_{1}^{2} k_{2}^{4} - k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left(2 \, {\left(k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(3 \, k_{1}^{6} + 7 \, k_{1}^{5} k_{2} + k_{1}^{4} k_{2}^{2} - 6 \, k_{1}^{3} k_{2}^{3} + k_{1}^{2} k_{2}^{4} + 7 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + 3 \, {\left({\left(k_{1}^{6} - 2 \, k_{1}^{5} k_{2} - k_{1}^{4} k_{2}^{2} + 4 \, k_{1}^{3} k_{2}^{3} - k_{1}^{2} k_{2}^{4} - 2 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left({\left(2 \, k_{1} + 3 \, k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{6} + 2 \, k_{1}^{5} k_{2} - k_{1}^{4} k_{2}^{2} - 4 \, k_{1}^{3} k_{2}^{3} - k_{1}^{2} k_{2}^{4} + 2 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left({\left(k_{1} + 3 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(3 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left({\left(3 \, k_{1}^{6} + 8 \, k_{1}^{5} k_{2} + 5 \, k_{1}^{4} k_{2}^{2} + 5 \, k_{1}^{2} k_{2}^{4} + 8 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(k_{1} + k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(3 \, k_{1}^{6} + 4 \, k_{1}^{5} k_{2} - 11 \, k_{1}^{4} k_{2}^{2} - 24 \, k_{1}^{3} k_{2}^{3} - 11 \, k_{1}^{2} k_{2}^{4} + 4 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(2 \, k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(\beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} D[0]\left(\alpha\right)\left(x, t_{1}, t_{2}, t_{3}\right)\right)} D[0, 0]\left(\alpha\right)\left(x, t_{1}, t_{2}, t_{3}\right) + 3 \, {\left(2 \, {\left({\left({\left(3 \, k_{1}^{6} + 4 \, k_{1}^{5} k_{2} - 11 \, k_{1}^{4} k_{2}^{2} - 24 \, k_{1}^{3} k_{2}^{3} - 11 \, k_{1}^{2} k_{2}^{4} + 4 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(3 \, k_{1}^{6} + 8 \, k_{1}^{5} k_{2} - 3 \, k_{1}^{4} k_{2}^{2} - 16 \, k_{1}^{3} k_{2}^{3} - 3 \, k_{1}^{2} k_{2}^{4} + 8 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left(2 \, {\left(k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left({\left(3 \, k_{1}^{6} + 8 \, k_{1}^{5} k_{2} + 5 \, k_{1}^{4} k_{2}^{2} + 5 \, k_{1}^{2} k_{2}^{4} + 8 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(k_{1} + k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(3 \, k_{1}^{6} + 16 \, k_{1}^{5} k_{2} + 37 \, k_{1}^{4} k_{2}^{2} + 48 \, k_{1}^{3} k_{2}^{3} + 37 \, k_{1}^{2} k_{2}^{4} + 16 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(2 \, k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(\beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} D[0]\left(\alpha\right)\left(x, t_{1}, t_{2}, t_{3}\right)^{2} + 2 \, {\left({\left(3 \, {\left(k_{1}^{6} - 2 \, k_{1}^{5} k_{2} - k_{1}^{4} k_{2}^{2} + 4 \, k_{1}^{3} k_{2}^{3} - k_{1}^{2} k_{2}^{4} - 2 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left({\left(3 \, k_{1} + 2 \, k_{2}\right)} x + 3 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + 2 \, {\left(3 \, k_{1}^{6} - k_{1}^{5} k_{2} - 3 \, k_{1}^{4} k_{2}^{2} + 2 \, k_{1}^{3} k_{2}^{3} - 3 \, k_{1}^{2} k_{2}^{4} - k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left(2 \, {\left(k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(3 \, k_{1}^{6} + 4 \, k_{1}^{5} k_{2} - 11 \, k_{1}^{4} k_{2}^{2} - 24 \, k_{1}^{3} k_{2}^{3} - 11 \, k_{1}^{2} k_{2}^{4} + 4 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left({\left(3 \, k_{1}^{6} + 8 \, k_{1}^{5} k_{2} + 5 \, k_{1}^{4} k_{2}^{2} + 5 \, k_{1}^{2} k_{2}^{4} + 8 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(k_{1} + k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + 3 \, {\left(k_{1}^{6} + 2 \, k_{1}^{5} k_{2} - k_{1}^{4} k_{2}^{2} - 4 \, k_{1}^{3} k_{2}^{3} - k_{1}^{2} k_{2}^{4} + 2 \, k_{1} k_{2}^{5} + k_{2}^{6}\right)} e^{\left({\left(3 \, k_{1} + k_{2}\right)} x + 3 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + 2 \, {\left(3 \, k_{1}^{6} + 7 \, k_{1}^{5} k_{2} + k_{1}^{4} k_{2}^{2} - 6 \, k_{1}^{3} k_{2}^{3} + k_{1}^{2} k_{2}^{4} + 7 \, k_{1} k_{2}^{5} + 3 \, k_{2}^{6}\right)} e^{\left({\left(2 \, k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(\beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} D[0, 0]\left(\alpha\right)\left(x, t_{1}, t_{2}, t_{3}\right) + 4 \, {\left({\left({\left(3 \, k_{1}^{7} + 8 \, k_{1}^{6} k_{2} - 5 \, k_{1}^{5} k_{2}^{2} - 40 \, k_{1}^{4} k_{2}^{3} - 55 \, k_{1}^{3} k_{2}^{4} - 32 \, k_{1}^{2} k_{2}^{5} - 7 \, k_{1} k_{2}^{6}\right)} e^{\left({\left(k_{1} + k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(3 \, k_{1}^{7} + 16 \, k_{1}^{6} k_{2} + 27 \, k_{1}^{5} k_{2}^{2} + 8 \, k_{1}^{4} k_{2}^{3} - 23 \, k_{1}^{3} k_{2}^{4} - 24 \, k_{1}^{2} k_{2}^{5} - 7 \, k_{1} k_{2}^{6}\right)} e^{\left({\left(2 \, k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(\beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left({\left(3 \, k_{1}^{7} + 4 \, k_{1}^{6} k_{2} - 9 \, k_{1}^{5} k_{2}^{2} - 16 \, k_{1}^{4} k_{2}^{3} + k_{1}^{3} k_{2}^{4} + 12 \, k_{1}^{2} k_{2}^{5} + 5 \, k_{1} k_{2}^{6}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(3 \, k_{1}^{7} + 8 \, k_{1}^{6} k_{2} - k_{1}^{5} k_{2}^{2} - 16 \, k_{1}^{4} k_{2}^{3} - 7 \, k_{1}^{3} k_{2}^{4} + 8 \, k_{1}^{2} k_{2}^{5} + 5 \, k_{1} k_{2}^{6}\right)} e^{\left(2 \, {\left(k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} D[0]\left(\alpha\right)\left(x, t_{1}, t_{2}, t_{3}\right) + {\left(5 \, {\left(k_{1}^{6} k_{2}^{2} + 2 \, k_{1}^{5} k_{2}^{3} - k_{1}^{4} k_{2}^{4} - 4 \, k_{1}^{3} k_{2}^{5} - k_{1}^{2} k_{2}^{6} + 2 \, k_{1} k_{2}^{7} + k_{2}^{8}\right)} e^{\left({\left(3 \, k_{1} + k_{2}\right)} x + 3 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + 5 \, {\left(k_{1}^{6} k_{2}^{2} + 6 \, k_{1}^{5} k_{2}^{3} + 15 \, k_{1}^{4} k_{2}^{4} + 20 \, k_{1}^{3} k_{2}^{5} + 15 \, k_{1}^{2} k_{2}^{6} + 6 \, k_{1} k_{2}^{7} + k_{2}^{8}\right)} e^{\left(k_{2} x\right)} + {\left(6 \, k_{1}^{8} + 16 \, k_{1}^{7} k_{2} - 15 \, k_{1}^{6} k_{2}^{2} - 90 \, k_{1}^{5} k_{2}^{3} - 85 \, k_{1}^{4} k_{2}^{4} + 36 \, k_{1}^{3} k_{2}^{5} + 111 \, k_{1}^{2} k_{2}^{6} + 70 \, k_{1} k_{2}^{7} + 15 \, k_{2}^{8}\right)} e^{\left({\left(k_{1} + k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(6 \, k_{1}^{8} + 32 \, k_{1}^{7} k_{2} + 49 \, k_{1}^{6} k_{2}^{2} - 14 \, k_{1}^{5} k_{2}^{3} - 101 \, k_{1}^{4} k_{2}^{4} - 68 \, k_{1}^{3} k_{2}^{5} + 31 \, k_{1}^{2} k_{2}^{6} + 50 \, k_{1} k_{2}^{7} + 15 \, k_{2}^{8}\right)} e^{\left({\left(2 \, k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(\beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left({\left(k_{1}^{6} k_{2}^{2} - 2 \, k_{1}^{5} k_{2}^{3} - k_{1}^{4} k_{2}^{4} + 4 \, k_{1}^{3} k_{2}^{5} - k_{1}^{2} k_{2}^{6} - 2 \, k_{1} k_{2}^{7} + k_{2}^{8}\right)} e^{\left({\left(3 \, k_{1} + 2 \, k_{2}\right)} x + 3 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} + {\left(k_{1}^{6} k_{2}^{2} + 6 \, k_{1}^{5} k_{2}^{3} + 15 \, k_{1}^{4} k_{2}^{4} + 20 \, k_{1}^{3} k_{2}^{5} + 15 \, k_{1}^{2} k_{2}^{6} + 6 \, k_{1} k_{2}^{7} + k_{2}^{8}\right)} e^{\left(2 \, k_{2} x\right)} - {\left(6 \, k_{1}^{8} + 8 \, k_{1}^{7} k_{2} - 17 \, k_{1}^{6} k_{2}^{2} - 26 \, k_{1}^{5} k_{2}^{3} + 13 \, k_{1}^{4} k_{2}^{4} + 28 \, k_{1}^{3} k_{2}^{5} + k_{1}^{2} k_{2}^{6} - 10 \, k_{1} k_{2}^{7} - 3 \, k_{2}^{8}\right)} e^{\left({\left(k_{1} + 2 \, k_{2}\right)} x + \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)} - {\left(6 \, k_{1}^{8} + 16 \, k_{1}^{7} k_{2} - k_{1}^{6} k_{2}^{2} - 34 \, k_{1}^{5} k_{2}^{3} - 19 \, k_{1}^{4} k_{2}^{4} + 20 \, k_{1}^{3} k_{2}^{5} + 17 \, k_{1}^{2} k_{2}^{6} - 2 \, k_{1} k_{2}^{7} - 3 \, k_{2}^{8}\right)} e^{\left(2 \, {\left(k_{1} + k_{2}\right)} x + 2 \, \alpha\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} e^{\left(2 \, \beta\left(x, t_{1}, t_{2}, t_{3}\right)\right)}\right)} D[0]\left(\beta\right)\left(x, t_{1}, t_{2}, t_{3}\right)\right)} D[0, 0]\left(\beta\right)\left(x, t_{1}, t_{2}, t_{3}\right)

full_output.txt

Ut2 = diff(U,t2).simplify_exp() RHSt2 = (30*U^2*Ux + 20*Ux*Uxx + 10*U*Uxxx + Uxxxxx).simplify_full()

%hide %html <h1>Exercise 6</h1> This first attempt demonstrates some ambiguous notation in Sage when it comes to taking the derivative of a conjugated function. Scroll down to the next comment to see the "fo' reals" computation.

Exercise 6

This first attempt demonstrates some ambiguous notation in Sage when it comes to taking the derivative of a conjugated function. Scroll down to the next comment to see the "fo' reals" computation.

Exercise 6

This first attempt demonstrates some ambiguous notation in Sage when it comes to taking the derivative of a conjugated function. Scroll down to the next comment to see the "fo' reals" computation.

var('x,t,zeta') q = function('q',x,t) sign = 1 def ex6_lax_pair(sign=1): X = matrix(SR,2,2,[-I*zeta, q, sign*q.conjugate(), i*zeta]) T = matrix(SR,2,2,[-I*zeta^2 - sign*I/2*q*q.conjugate(), q*zeta + I/2*q.derivative(x), sign*q.conjugate()*zeta - sign*I/2*q.derivative(x).conjugate(), I*zeta^2 + sign*I/2*q*q.conjugate()]) return X,T

X,T = ex6_lax_pair() show(X) show(T)

\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rr}
-i \, \zeta & q\left(x, t\right) \\
\overline{q\left(x, t\right)} & i \, \zeta
\end{array}\right)
\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rr}
-i \, \zeta^{2} - \frac{1}{2} i \, \overline{q\left(x, t\right)} q\left(x, t\right) & \zeta q\left(x, t\right) + \frac{1}{2} i \, D[0]\left(q\right)\left(x, t\right) \\
\zeta \overline{q\left(x, t\right)} - \frac{1}{2} i \, \overline{D[0]\left(q\right)\left(x, t\right)} & i \, \zeta^{2} + \frac{1}{2} i \, \overline{q\left(x, t\right)} q\left(x, t\right)
\end{array}\right)

\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rr}
-i \, \zeta & q\left(x, t\right) \\
\overline{q\left(x, t\right)} & i \, \zeta
\end{array}\right)
\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rr}
-i \, \zeta^{2} - \frac{1}{2} i \, \overline{q\left(x, t\right)} q\left(x, t\right) & \zeta q\left(x, t\right) + \frac{1}{2} i \, D[0]\left(q\right)\left(x, t\right) \\
\zeta \overline{q\left(x, t\right)} - \frac{1}{2} i \, \overline{D[0]\left(q\right)\left(x, t\right)} & i \, \zeta^{2} + \frac{1}{2} i \, \overline{q\left(x, t\right)} q\left(x, t\right)
\end{array}\right)

LHS = X.apply_map(lambda y: y.derivative(t)) - T.apply_map(lambda y: y.derivative(x)) RHS = T*X - X*T Z = LHS - RHS show(Z)

\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rr}
\frac{1}{2} i \, q\left(x, t\right) D[0]\left({\rm conjugate}\right)\left(q\left(x, t\right)\right) D[0]\left(q\right)\left(x, t\right) - \frac{1}{2} \, {\left(2 \, \zeta q\left(x, t\right) + i \, D[0]\left(q\right)\left(x, t\right)\right)} \overline{q\left(x, t\right)} + \frac{1}{2} \, {\left(2 \, \zeta \overline{q\left(x, t\right)} - i \, \overline{D[0]\left(q\right)\left(x, t\right)}\right)} q\left(x, t\right) + \frac{1}{2} i \, \overline{q\left(x, t\right)} D[0]\left(q\right)\left(x, t\right) & -i \, {\left(2 \, \zeta q\left(x, t\right) + i \, D[0]\left(q\right)\left(x, t\right)\right)} \zeta - \frac{1}{2} \, {\left(-2 i \, \zeta^{2} - i \, \overline{q\left(x, t\right)} q\left(x, t\right)\right)} q\left(x, t\right) + \frac{1}{2} \, {\left(2 i \, \zeta^{2} + i \, \overline{q\left(x, t\right)} q\left(x, t\right)\right)} q\left(x, t\right) - \zeta D[0]\left(q\right)\left(x, t\right) - \frac{1}{2} i \, D[0, 0]\left(q\right)\left(x, t\right) + D[1]\left(q\right)\left(x, t\right) \\
-\zeta D[0]\left({\rm conjugate}\right)\left(q\left(x, t\right)\right) D[0]\left(q\right)\left(x, t\right) + i \, {\left(2 \, \zeta \overline{q\left(x, t\right)} - i \, \overline{D[0]\left(q\right)\left(x, t\right)}\right)} \zeta + \frac{1}{2} \, {\left(-2 i \, \zeta^{2} - i \, \overline{q\left(x, t\right)} q\left(x, t\right)\right)} \overline{q\left(x, t\right)} - \frac{1}{2} \, {\left(2 i \, \zeta^{2} + i \, \overline{q\left(x, t\right)} q\left(x, t\right)\right)} \overline{q\left(x, t\right)} + D[0]\left({\rm conjugate}\right)\left(q\left(x, t\right)\right) D[1]\left(q\right)\left(x, t\right) + \frac{1}{2} i \, D[0]\left({\rm conjugate}\right)\left(D[0]\left(q\right)\left(x, t\right)\right) D[0, 0]\left(q\right)\left(x, t\right) & -\frac{1}{2} i \, q\left(x, t\right) D[0]\left({\rm conjugate}\right)\left(q\left(x, t\right)\right) D[0]\left(q\right)\left(x, t\right) + \frac{1}{2} \, {\left(2 \, \zeta q\left(x, t\right) + i \, D[0]\left(q\right)\left(x, t\right)\right)} \overline{q\left(x, t\right)} - \frac{1}{2} \, {\left(2 \, \zeta \overline{q\left(x, t\right)} - i \, \overline{D[0]\left(q\right)\left(x, t\right)}\right)} q\left(x, t\right) - \frac{1}{2} i \, \overline{q\left(x, t\right)} D[0]\left(q\right)\left(x, t\right)
\end{array}\right)

\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rr}
\frac{1}{2} i \, q\left(x, t\right) D[0]\left({\rm conjugate}\right)\left(q\left(x, t\right)\right) D[0]\left(q\right)\left(x, t\right) - \frac{1}{2} \, {\left(2 \, \zeta q\left(x, t\right) + i \, D[0]\left(q\right)\left(x, t\right)\right)} \overline{q\left(x, t\right)} + \frac{1}{2} \, {\left(2 \, \zeta \overline{q\left(x, t\right)} - i \, \overline{D[0]\left(q\right)\left(x, t\right)}\right)} q\left(x, t\right) + \frac{1}{2} i \, \overline{q\left(x, t\right)} D[0]\left(q\right)\left(x, t\right) & -i \, {\left(2 \, \zeta q\left(x, t\right) + i \, D[0]\left(q\right)\left(x, t\right)\right)} \zeta - \frac{1}{2} \, {\left(-2 i \, \zeta^{2} - i \, \overline{q\left(x, t\right)} q\left(x, t\right)\right)} q\left(x, t\right) + \frac{1}{2} \, {\left(2 i \, \zeta^{2} + i \, \overline{q\left(x, t\right)} q\left(x, t\right)\right)} q\left(x, t\right) - \zeta D[0]\left(q\right)\left(x, t\right) - \frac{1}{2} i \, D[0, 0]\left(q\right)\left(x, t\right) + D[1]\left(q\right)\left(x, t\right) \\
-\zeta D[0]\left({\rm conjugate}\right)\left(q\left(x, t\right)\right) D[0]\left(q\right)\left(x, t\right) + i \, {\left(2 \, \zeta \overline{q\left(x, t\right)} - i \, \overline{D[0]\left(q\right)\left(x, t\right)}\right)} \zeta + \frac{1}{2} \, {\left(-2 i \, \zeta^{2} - i \, \overline{q\left(x, t\right)} q\left(x, t\right)\right)} \overline{q\left(x, t\right)} - \frac{1}{2} \, {\left(2 i \, \zeta^{2} + i \, \overline{q\left(x, t\right)} q\left(x, t\right)\right)} \overline{q\left(x, t\right)} + D[0]\left({\rm conjugate}\right)\left(q\left(x, t\right)\right) D[1]\left(q\right)\left(x, t\right) + \frac{1}{2} i \, D[0]\left({\rm conjugate}\right)\left(D[0]\left(q\right)\left(x, t\right)\right) D[0, 0]\left(q\right)\left(x, t\right) & -\frac{1}{2} i \, q\left(x, t\right) D[0]\left({\rm conjugate}\right)\left(q\left(x, t\right)\right) D[0]\left(q\right)\left(x, t\right) + \frac{1}{2} \, {\left(2 \, \zeta q\left(x, t\right) + i \, D[0]\left(q\right)\left(x, t\right)\right)} \overline{q\left(x, t\right)} - \frac{1}{2} \, {\left(2 \, \zeta \overline{q\left(x, t\right)} - i \, \overline{D[0]\left(q\right)\left(x, t\right)}\right)} q\left(x, t\right) - \frac{1}{2} i \, \overline{q\left(x, t\right)} D[0]\left(q\right)\left(x, t\right)
\end{array}\right)

Z = Z.apply_map(lambda y: y.simplify()) show(Z)

Traceback (click to the left of this block for traceback)
...
NotImplementedError: arguments must be distinct variables

Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "_sage_input_6.py", line 10, in <module>
    exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("WiA9IFouYXBwbHlfbWFwKGxhbWJkYSB5OiB5LnNpbXBsaWZ5KCkpCnNob3coWik="),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))
  File "", line 1, in <module>
    
  File "/tmp/tmpk1E8ec/___code___.py", line 2, in <module>
    Z = Z.apply_map(lambda y: y.simplify())
  File "matrix_dense.pyx", line 418, in sage.matrix.matrix_dense.Matrix_dense.apply_map (sage/matrix/matrix_dense.c:4089)
  File "/tmp/tmpk1E8ec/___code___.py", line 2, in <lambda>
    Z = Z.apply_map(lambda y: y.simplify())
  File "expression.pyx", line 6347, in sage.symbolic.expression.Expression.simplify (sage/symbolic/expression.cpp:23472)
  File "expression.pyx", line 446, in sage.symbolic.expression.Expression._maxima_ (sage/symbolic/expression.cpp:3592)
  File "sage_object.pyx", line 379, in sage.structure.sage_object.SageObject._interface_ (sage/structure/sage_object.c:3317)
  File "sage_object.pyx", line 468, in sage.structure.sage_object.SageObject._maxima_init_ (sage/structure/sage_object.c:5019)
  File "expression.pyx", line 471, in sage.symbolic.expression.Expression._interface_init_ (sage/symbolic/expression.cpp:3718)
  File "/home/sage/sage_install/sage-4.6/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.py", line 214, in __call__
    return self.arithmetic(ex, operator)
  File "/home/sage/sage_install/sage-4.6/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.py", line 515, in arithmetic
    args = ["(%s)"%self(op) for op in ex.operands()]
  File "/home/sage/sage_install/sage-4.6/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.py", line 214, in __call__
    return self.arithmetic(ex, operator)
  File "/home/sage/sage_install/sage-4.6/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.py", line 515, in arithmetic
    args = ["(%s)"%self(op) for op in ex.operands()]
  File "/home/sage/sage_install/sage-4.6/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.py", line 218, in __call__
    return self.derivative(ex, operator)
  File "/home/sage/sage_install/sage-4.6/local/lib/python2.6/site-packages/sage/symbolic/expression_conversions.py", line 495, in derivative
    raise NotImplementedError, "arguments must be distinct variables"
NotImplementedError: arguments must be distinct variables

show(LHS)

\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rr}
\frac{1}{2} i \, q\left(x, t\right) D[0]\left({\rm conjugate}\right)\left(q\left(x, t\right)\right) D[0]\left(q\right)\left(x, t\right) + \frac{1}{2} i \, \overline{q\left(x, t\right)} D[0]\left(q\right)\left(x, t\right) & -\zeta D[0]\left(q\right)\left(x, t\right) - \frac{1}{2} i \, D[0, 0]\left(q\right)\left(x, t\right) + D[1]\left(q\right)\left(x, t\right) \\
-\zeta D[0]\left({\rm conjugate}\right)\left(q\left(x, t\right)\right) D[0]\left(q\right)\left(x, t\right) + D[0]\left({\rm conjugate}\right)\left(q\left(x, t\right)\right) D[1]\left(q\right)\left(x, t\right) + \frac{1}{2} i \, D[0]\left({\rm conjugate}\right)\left(D[0]\left(q\right)\left(x, t\right)\right) D[0, 0]\left(q\right)\left(x, t\right) & -\frac{1}{2} i \, q\left(x, t\right) D[0]\left({\rm conjugate}\right)\left(q\left(x, t\right)\right) D[0]\left(q\right)\left(x, t\right) - \frac{1}{2} i \, \overline{q\left(x, t\right)} D[0]\left(q\right)\left(x, t\right)
\end{array}\right)

\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rr}
\frac{1}{2} i \, q\left(x, t\right) D[0]\left({\rm conjugate}\right)\left(q\left(x, t\right)\right) D[0]\left(q\right)\left(x, t\right) + \frac{1}{2} i \, \overline{q\left(x, t\right)} D[0]\left(q\right)\left(x, t\right) & -\zeta D[0]\left(q\right)\left(x, t\right) - \frac{1}{2} i \, D[0, 0]\left(q\right)\left(x, t\right) + D[1]\left(q\right)\left(x, t\right) \\
-\zeta D[0]\left({\rm conjugate}\right)\left(q\left(x, t\right)\right) D[0]\left(q\right)\left(x, t\right) + D[0]\left({\rm conjugate}\right)\left(q\left(x, t\right)\right) D[1]\left(q\right)\left(x, t\right) + \frac{1}{2} i \, D[0]\left({\rm conjugate}\right)\left(D[0]\left(q\right)\left(x, t\right)\right) D[0, 0]\left(q\right)\left(x, t\right) & -\frac{1}{2} i \, q\left(x, t\right) D[0]\left({\rm conjugate}\right)\left(q\left(x, t\right)\right) D[0]\left(q\right)\left(x, t\right) - \frac{1}{2} i \, \overline{q\left(x, t\right)} D[0]\left(q\right)\left(x, t\right)
\end{array}\right)

RHS = RHS.apply_map(lambda y: y.simplify_full()) show(RHS)

\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rr}
\frac{1}{2} i \, \overline{q\left(x, t\right)} D[0]\left(q\right)\left(x, t\right) + \frac{1}{2} i \, \overline{D[0]\left(q\right)\left(x, t\right)} q\left(x, t\right) & -i \, \overline{q\left(x, t\right)} q\left(x, t\right)^{2} - \zeta D[0]\left(q\right)\left(x, t\right) \\
i \, \overline{q\left(x, t\right)}^{2} q\left(x, t\right) - \zeta \overline{D[0]\left(q\right)\left(x, t\right)} & -\frac{1}{2} i \, \overline{q\left(x, t\right)} D[0]\left(q\right)\left(x, t\right) - \frac{1}{2} i \, \overline{D[0]\left(q\right)\left(x, t\right)} q\left(x, t\right)
\end{array}\right)

\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rr}
\frac{1}{2} i \, \overline{q\left(x, t\right)} D[0]\left(q\right)\left(x, t\right) + \frac{1}{2} i \, \overline{D[0]\left(q\right)\left(x, t\right)} q\left(x, t\right) & -i \, \overline{q\left(x, t\right)} q\left(x, t\right)^{2} - \zeta D[0]\left(q\right)\left(x, t\right) \\
i \, \overline{q\left(x, t\right)}^{2} q\left(x, t\right) - \zeta \overline{D[0]\left(q\right)\left(x, t\right)} & -\frac{1}{2} i \, \overline{q\left(x, t\right)} D[0]\left(q\right)\left(x, t\right) - \frac{1}{2} i \, \overline{D[0]\left(q\right)\left(x, t\right)} q\left(x, t\right)
\end{array}\right)

# demonstrating a bug in Sage var('x,t') q = function('q',x,t) f = q*q.conjugate() show(f) print f.derivative(x,1) print q.conjugate().derivative(x,1) print q.derivative(x,1).conjugate()

\newcommand{\Bold}[1]{\mathbf{#1}}\overline{q\left(x, t\right)} q\left(x, t\right)

\newcommand{\Bold}[1]{\mathbf{#1}}\overline{q\left(x, t\right)} q\left(x, t\right)

%hide %html <h3>Note:</h3> There seems to be a bug with differentiating conjugated function in Sage. So I'm going to try something else, namely, let $\bar{q}$ be a separate variable called <tt>qbar</tt>:

Note:

There seems to be a bug with differentiating conjugated function in Sage. So I'm going to try something else, namely, let \bar{q} be a separate variable called qbar:

Note:

There seems to be a bug with differentiating conjugated function in Sage. So I'm going to try something else, namely, let \bar{q} be a separate variable called qbar:

var('x,t,zeta') q = function('q',x,t) qbar = function('qbar',x,t) def ex6_lax_pair(sign=1): X = matrix(SR,2,2,[-I*zeta, q, sign*qbar, i*zeta]) T = matrix(SR,2,2,[-I*zeta^2 - sign*I/2*q*qbar, q*zeta + I/2*q.derivative(x), sign*qbar*zeta - sign*I/2*qbar.derivative(x), I*zeta^2 + sign*I/2*q*qbar]) return X,T

X,T = ex6_lax_pair(1) LHS = X.derivative(t) - T.derivative(x) RHS = T*X - X*T

LHS = LHS.apply_map(lambda y: y.simplify_full()) RHS = RHS.apply_map(lambda y: y.simplify_full())

show(LHS)

\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rr}
\frac{1}{2} i \, q\left(x, t\right) D[0]\left({\rm qbar}\right)\left(x, t\right) + \frac{1}{2} i \, {\rm qbar}\left(x, t\right) D[0]\left(q\right)\left(x, t\right) & -\zeta D[0]\left(q\right)\left(x, t\right) - \frac{1}{2} i \, D[0, 0]\left(q\right)\left(x, t\right) + D[1]\left(q\right)\left(x, t\right) \\
-\zeta D[0]\left({\rm qbar}\right)\left(x, t\right) + \frac{1}{2} i \, D[0, 0]\left({\rm qbar}\right)\left(x, t\right) + D[1]\left({\rm qbar}\right)\left(x, t\right) & -\frac{1}{2} i \, q\left(x, t\right) D[0]\left({\rm qbar}\right)\left(x, t\right) - \frac{1}{2} i \, {\rm qbar}\left(x, t\right) D[0]\left(q\right)\left(x, t\right)
\end{array}\right)

\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rr}
\frac{1}{2} i \, q\left(x, t\right) D[0]\left({\rm qbar}\right)\left(x, t\right) + \frac{1}{2} i \, {\rm qbar}\left(x, t\right) D[0]\left(q\right)\left(x, t\right) & -\zeta D[0]\left(q\right)\left(x, t\right) - \frac{1}{2} i \, D[0, 0]\left(q\right)\left(x, t\right) + D[1]\left(q\right)\left(x, t\right) \\
-\zeta D[0]\left({\rm qbar}\right)\left(x, t\right) + \frac{1}{2} i \, D[0, 0]\left({\rm qbar}\right)\left(x, t\right) + D[1]\left({\rm qbar}\right)\left(x, t\right) & -\frac{1}{2} i \, q\left(x, t\right) D[0]\left({\rm qbar}\right)\left(x, t\right) - \frac{1}{2} i \, {\rm qbar}\left(x, t\right) D[0]\left(q\right)\left(x, t\right)
\end{array}\right)

show(RHS)

\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rr}
\frac{1}{2} i \, q\left(x, t\right) D[0]\left({\rm qbar}\right)\left(x, t\right) + \frac{1}{2} i \, {\rm qbar}\left(x, t\right) D[0]\left(q\right)\left(x, t\right) & -i \, q\left(x, t\right)^{2} {\rm qbar}\left(x, t\right) - \zeta D[0]\left(q\right)\left(x, t\right) \\
i \, q\left(x, t\right) {\rm qbar}\left(x, t\right)^{2} - \zeta D[0]\left({\rm qbar}\right)\left(x, t\right) & -\frac{1}{2} i \, q\left(x, t\right) D[0]\left({\rm qbar}\right)\left(x, t\right) - \frac{1}{2} i \, {\rm qbar}\left(x, t\right) D[0]\left(q\right)\left(x, t\right)
\end{array}\right)

\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rr}
\frac{1}{2} i \, q\left(x, t\right) D[0]\left({\rm qbar}\right)\left(x, t\right) + \frac{1}{2} i \, {\rm qbar}\left(x, t\right) D[0]\left(q\right)\left(x, t\right) & -i \, q\left(x, t\right)^{2} {\rm qbar}\left(x, t\right) - \zeta D[0]\left(q\right)\left(x, t\right) \\
i \, q\left(x, t\right) {\rm qbar}\left(x, t\right)^{2} - \zeta D[0]\left({\rm qbar}\right)\left(x, t\right) & -\frac{1}{2} i \, q\left(x, t\right) D[0]\left({\rm qbar}\right)\left(x, t\right) - \frac{1}{2} i \, {\rm qbar}\left(x, t\right) D[0]\left(q\right)\left(x, t\right)
\end{array}\right)

show((LHS-RHS).apply_map(lambda y: y.simplify_full()))

\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rr}
0 & i \, q\left(x, t\right)^{2} {\rm qbar}\left(x, t\right) - \frac{1}{2} i \, D[0, 0]\left(q\right)\left(x, t\right) + D[1]\left(q\right)\left(x, t\right) \\
-i \, q\left(x, t\right) {\rm qbar}\left(x, t\right)^{2} + \frac{1}{2} i \, D[0, 0]\left({\rm qbar}\right)\left(x, t\right) + D[1]\left({\rm qbar}\right)\left(x, t\right) & 0
\end{array}\right)

\newcommand{\Bold}[1]{\mathbf{#1}}\left(\begin{array}{rr}
0 & i \, q\left(x, t\right)^{2} {\rm qbar}\left(x, t\right) - \frac{1}{2} i \, D[0, 0]\left(q\right)\left(x, t\right) + D[1]\left(q\right)\left(x, t\right) \\
-i \, q\left(x, t\right) {\rm qbar}\left(x, t\right)^{2} + \frac{1}{2} i \, D[0, 0]\left({\rm qbar}\right)\left(x, t\right) + D[1]\left({\rm qbar}\right)\left(x, t\right) & 0
\end{array}\right)

%hide %html <h1>Exercise 7</h1>

Exercise 7

# # I ended up doing this by hand. See the homework. # var('x,t,zeta') q = function('q',x,t) qbar = function('qbar',x,t) def ex6_lax_pair(sign=1): X = matrix(SR,2,2,[-I*zeta, q, sign*qbar, i*zeta]) T = matrix(SR,2,2,[-I*zeta^2 - sign*I/2*q*qbar, q*zeta + I/2*q.derivative(x), sign*qbar*zeta - sign*I/2*qbar.derivative(x), I*zeta^2 + sign*I/2*q*qbar]) return X,T

var('x,t,z') q_nm1 = function('q_nm1',x,t) q_n = function('q_n',x,t) q_np1 = function('q_np1',x,t) qbar_n = function('qbar_n',x,t) qbar_nm1 = function('qbar_ show([q_nm1,q_n,q_np1])

\newcommand{\Bold}[1]{\mathbf{#1}}\left[q_{{\rm nm}_{1}}\left(x, t\right), q_{n}\left(x, t\right), q_{{\rm np}_{1}}\left(x, t\right)\right]

\newcommand{\Bold}[1]{\mathbf{#1}}\left[q_{{\rm nm}_{1}}\left(x, t\right), q_{n}\left(x, t\right), q_{{\rm np}_{1}}\left(x, t\right)\right]

X_n = matrix(SR,2,2,[z, q_n,

var('x') u = function('u',x) ux = diff(u,x)

ux.integrate(x)

\newcommand{\Bold}[1]{\mathbf{#1}}u\left(x\right)

\newcommand{\Bold}[1]{\mathbf{#1}}u\left(x\right)

AMath 573 - Homework 4

540 days ago by cswiercz

Exercise 1

Exercise 1

Exercise 4

Exercise 4

Exercise 5

Exercise 5

Exercise 6

Exercise 6

Note:

Note:

Exercise 7

Exercise 7