Added December 27, 2018.
Taken from https://en.wikipedia.org/wiki/List_of_nonlinear_partial_differential_equations
Bateman-Burgers.
Solve for \(u(x,t)\)
\[ u_t+u u_x = \nu u_{xx} \]
Mathematica ✓
ClearAll["Global`*"]; pde = D[u[x, t], t] + u[x, t]*D[u[x, t], x] == v*D[u[x, t], {x, 2}]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, u[x, t], {x, t}], 60*10]];
\[\left \{\left \{u(x,t)\to -2 c_1 v \tanh (c_2 t+c_1 x+c_3)-\frac {c_2}{c_1}\right \}\right \}\]
Maple ✓
restart; pde := diff(u(x,t),t)+u(x,t)*diff(u(x,t),x)=v*diff(u(x,t),x$2); cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,u(x,t))),output='realtime'));
\[u \left (x , t\right ) = \frac {-2 c_{2}^{2} v \tanh \left (c_{3} t +c_{2} x +c_{1}\right )-c_{3}}{c_{2}}\]
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