Added December 27, 2018.
Taken from https://en.wikipedia.org/wiki/List_of_nonlinear_partial_differential_equations
Rayleigh. Solve for \(u(x,t)\) \[ u_{tt} - u_{xx} = \epsilon (u_t - u_t^3) \]
Mathematica ✗
ClearAll["Global`*"]; pde = D[u[x, t], {t, 2}] - D[u[x, t], {x, 2}] == epsilon*(D[u[x, t], t] - D[u[x, t], t]^3); sol = AbsoluteTiming[TimeConstrained[DSolve[pde, u[x, t], {x, t}], 60*10]];
Failed
Maple ✓
restart; pde := diff(u(x,t),t$2)-diff(u(x,t),x$2)=epsilon*(diff(u(x,t),t)-diff(u(x,t),t)^3); cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,u(x,t),'build')),output='realtime'));
\[u \left ( x,t \right ) ={\frac {{\it \_c}_{{1}}{x}^{2}}{2}}+{\it \_C1}\,x+{\it \_C2}+\int \!\RootOf \left ( t+\int ^{{\it \_Z}}\! \left ( {{\it \_f}}^{3}\epsilon -{\it \_f}\,\epsilon -{\it \_c}_{{1}} \right ) ^{-1}{d{\it \_f}}+{\it \_C3} \right ) \,{\rm d}t+{\it \_C4}\] Has RootOf
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