Added December 27, 2018.
Taken from https://en.wikipedia.org/wiki/List_of_nonlinear_partial_differential_equations
Born Infeld. Solve for \(u(x,t)\) \[ (1-u_t^2) u_{xx} + 2 u_x u_t u_{xt} - (1+ u_x^2) u_{tt}=0 \]
Mathematica ✓
ClearAll["Global`*"]; pde = (1 - D[u[x, t], t]^2)*D[u[x, t], {x, 2}] + 2*D[u[x, t], x]*D[u[x, t], t]*D[D[u[x, t], x], t] - (1 + D[u[x, t], x]^2)*D[u[x, t], {t, 2}] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, u[x, t], {x, t}], 60*10]];
\[\{\{u(x,t)\to c_1(t+x)+c_2(t-x)\}\}\]
Maple ✓
restart; pde :=(1-diff(u(x,t),t)^2)*diff(u(x,t),x$2)+2*diff(u(x,t),x)*diff(u(x,t),t)*diff(u(x,t),x,t)-(1+diff(u(x,t),x)^2)*diff(u(x,t),t$2)=0; cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,u(x,t))),output='realtime'));
\[u \left ( x,t \right ) ={\it \_C7}\, \left ( \tanh \left ( \left ( -t+x \right ) {\it \_C2}+{\it \_C1} \right ) \right ) ^{3}+{\it \_C5}\,\tanh \left ( \left ( -t+x \right ) {\it \_C2}+{\it \_C1} \right ) +{\it \_C4}\]
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