Added December 27, 2018.
Taken from https://en.wikipedia.org/wiki/List_of_nonlinear_partial_differential_equations
Thomas equation. Solve for \(u(x,t)\) \[ u_{xy} + \alpha u_x + \beta u_y+ \nu u_x u_y =0 \]
Mathematica ✗
ClearAll["Global`*"]; pde = D[u[x, y], x, y] + alpha*D[u[x, y], x] + beta*D[u[x, y], y] + nu*D[u[x, y], x]*D[u[x, y], y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, u[x, y], {x, y}], 60*10]];
Failed
Maple ✓
restart; pde := diff(u(x,y),x,y)+alpha*diff(u(x,y),x)+beta*diff(u(x,y),y) +nu* diff(u(x,y),x)*diff(u(x,y),y)=0; cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,u(x,y),'build')),output='realtime'));
\[u \left (x , y\right ) = \frac {-2 \alpha y -2 \beta x -\ln \left (\frac {\alpha ^{2}-2 \alpha \beta +\beta ^{2}-4 \textit {\_c}_{1} \nu }{\left (c_{1} {\mathrm e}^{\left (x -y \right ) \sqrt {\alpha ^{2}-2 \alpha \beta +\beta ^{2}-4 \textit {\_c}_{1} \nu }}-c_{2}\right )^{2} \nu ^{2}}\right )-\ln \left (\frac {\alpha ^{2}+2 \alpha \beta +\beta ^{2}-4 \textit {\_c}_{1} \nu }{\left (c_{3} {\mathrm e}^{\left (x +y \right ) \sqrt {\alpha ^{2}+2 \alpha \beta +\beta ^{2}-4 \textit {\_c}_{1} \nu }}-c_{4}\right )^{2} \nu ^{2}}\right )+\left (-x +y \right ) \sqrt {\alpha ^{2}-2 \alpha \beta +\beta ^{2}-4 \textit {\_c}_{1} \nu }+\left (-x -y \right ) \sqrt {\alpha ^{2}+2 \alpha \beta +\beta ^{2}-4 \textit {\_c}_{1} \nu }-4 \ln \left (2\right )}{2 \nu }\]
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