Added December 20, 2018.
Example 26, Taken from https://www.mapleprimes.com/posts/209970-Exact-Solutions-For-PDE-And-Boundary--Initial-Conditions-2018
Solve for \(w(x_1,x_2,x_3,t)\)
\[ \frac {\partial w}{\partial t} = \frac {\partial w^2}{\partial x_1 x_2} + \frac {\partial w^2}{\partial x_1 x_3} + \frac {\partial w^2}{\partial x_3^2} + \frac {\partial w^2}{\partial x_2 x_3} \]
With initial condition \(w(x_1,x_2,x_3,t_0) = e^{x_1} +x_2 -3 x_3\)
Mathematica ✓
ClearAll["Global`*"]; pde = D[w[x1, x2, x3, t], t] == D[w[x1, x2, x3, t], x1, x2] + D[w[x1, x2, x3, t], x1, x3] + D[w[x1, x2, x3, t], {x3, 2}] - D[w[x1, x2, x3, t], x2, x3]; ic = w[x1, x2, x3, t0] == Exp[x1] + x2 - 3*x3; sol = AbsoluteTiming[TimeConstrained[DSolve[{pde, ic}, w[x1, x2, x3, t], {x1, x2, x3, t}], 60*10]];
\[\left \{\left \{w(\text {x1},\text {x2},\text {x3},t)\to e^{\text {x1}}+\text {x2}-3 \text {x3}\right \}\right \}\]
Maple ✓
restart; pde := diff(w(x1, x2, x3, t), t)= diff(w(x1,x2,x3,t),x1,x2)+diff(w(x1,x2,x3,t),x1,x3)+diff(w(x1,x2,x3,t),x3$2)-diff(w(x1,x2,x3,t),x2,x3); ic := w(x1, x2, x3, t0) = exp(x1)+x2-3*x3; cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve([pde, ic],w(x1,x2,x3,t))),output='realtime'));
\[w \left ( {\it x1},{\it x2},{\it x3},t \right ) ={{\rm e}^{{\it x1}}}+{\it x2}-3\,{\it x3}\]
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