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