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'));
\[u \left ( x,t \right ) =\RootOf \left ( {\it \_C1}\,x+t{\it \_C2}+{\it \_C3}+\int ^{{\it \_Z}}\!4\,{\frac {{{\it \_C1}}^{2}{{\it \_f}}^{3}}{{\it \_C1}\,{{\it \_f}}^{3}+4\,{\it \_C3}\,{{\it \_C1}}^{2}-{\it \_C2}\,{\it \_f}}}{d{\it \_f}}+{\it \_C4} \right ) \] Answer in terms of RootOf.
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