Added December 27, 2018.
Taken from https://en.wikipedia.org/wiki/List_of_nonlinear_partial_differential_equations
Khokhlov Zabolotskaya. Solve for \(u(x,y,t)\) \[ u_{x t} - (u u_x)_x = u_{yy} \]
Mathematica ✗
ClearAll["Global`*"]; pde = D[D[u[x, y, t], x], t] - D[u[x, y, t]*D[u[x, y, t], x], x] == D[u[x, y, t], {y, 2}]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, u[x, y, t], {x, y, t}], 60*10]];
Failed
Maple ✓
restart; pde := diff(u(x,y,t),x,t)- diff( (u(x,y,t)* diff(u(x,y,t),x)) ,x ) = diff(u(x,y,t),y$2); cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,u(x,y,t))),output='realtime'));
\[u \left (x , y , t\right ) = \frac {c_{1} c_{3}-c_{2}^{2}+\sqrt {c_{1}^{2} c_{3}^{2}-2 c_{1} c_{2}^{2} c_{3}+c_{2}^{4}+2 c_{4} \left (c_{3} t +c_{1} x +c_{2} y +c_{4}\right ) c_{1}^{2}+2 c_{5} c_{1}^{2}}}{c_{1}^{2}}\]
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