Added December 27, 2018.
Taken from https://en.wikipedia.org/wiki/List_of_nonlinear_partial_differential_equations
Buckmaster. Solve for \(u(x,t)\) \[ u_t = (u^4)_{xx} + (u^3)_x \]
Mathematica ✗
ClearAll["Global`*"]; pde = D[u[x, t], t] == D[u[x, t]^4, {x, 2}] + D[u[x, t]^3, x]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, u[x, t], {x, t}], 60*10]];
Failed
Maple ✓
restart; pde := diff(u(x,t),t)= diff(u(x,t)^4,x$2)+diff(u(x,t)^3,x); cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,u(x,t))),output='realtime'));
\[u \left (x , t\right ) = \RootOf \left (c_{1} x +c_{2} t +c_{3}+c_{4}+\int _{}^{\textit {\_Z}}\frac {4 c_{1}^{2} \textit {\_f}^{3}}{c_{1} \textit {\_f}^{3}+4 c_{3} c_{1}^{2}-c_{2} \textit {\_f}}d \textit {\_f} \right )\] Answer in terms of RootOf.
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