Added December 27, 2018.
Taken from https://en.wikipedia.org/wiki/List_of_nonlinear_partial_differential_equations
Solve for \(u(x,t)\)
\[ u_t+u_x + u u+x - u_{xxt} = 0 \]
Mathematica ✓
ClearAll["Global`*"]; pde = D[u[x, t], t] + D[u[x, t], x] + u[x, t]*D[u[x, t], x] - D[D[u[x, t], {x, 2}], t] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, u[x, t], {x, t}], 60*10]];
\[\left \{\left \{u(x,t)\to 12 c_1 c_2 \tanh ^2(c_2 t+c_1 x+c_3)-1-8 c_1 c_2-\frac {c_2}{c_1}\right \}\right \}\]
Maple ✓
restart; pde := diff(u(x,t),t)+diff(u(x,t),x)+u(x,t)*diff(u(x,t),x)-diff(u(x,t),x,x,t)=0; cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,u(x,t))),output='realtime'));
\[u \left ( x,t \right ) ={\frac {12\,{\it \_C3}\,{{\it \_C2}}^{2} \left ( \tanh \left ( {\it \_C2}\,x+{\it \_C3}\,t+{\it \_C1} \right ) \right ) ^{2}-8\,{{\it \_C2}}^{2}{\it \_C3}-{\it \_C2}-{\it \_C3}}{{\it \_C2}}}\]
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