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'));
\[u \left (x , t\right ) = \frac {12 c_{3} c_{2}^{2} \left (\tanh ^{2}\left (c_{3} t +c_{2} x +c_{1}\right )\right )-8 c_{3} c_{2}^{2}-c_{2}-c_{3}}{c_{2}}\]
____________________________________________________________________________________