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'));
\[u \left ( x,y,t \right ) ={\frac {1}{{{\it \_C1}}^{2}} \left ( {\it \_C1}\,{\it \_C3}-{{\it \_C2}}^{2}+\sqrt {2\, \left ( {\it \_C1}\,x+{\it \_C2}\,y+{\it \_C3}\,t+{\it \_C4} \right ) {{\it \_C1}}^{2}{\it \_C4}+{{\it \_C1}}^{2}{{\it \_C3}}^{2}-2\,{\it \_C1}\,{{\it \_C2}}^{2}{\it \_C3}+{{\it \_C2}}^{4}+2\,{{\it \_C1}}^{2}{\it \_C5}} \right ) }\]
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