Added December 27, 2018.
Taken from https://en.wikipedia.org/wiki/List_of_nonlinear_partial_differential_equations
Plateau. Solve for \(u(x,y)\) \[ (1+u_y^2)u_{xx} - 2 u_x u_y y_{xy} + (1+u_x^2) u_{yy} = 0 \]
Mathematica ✗
ClearAll["Global`*"]; pde = (1 + D[u[x, y], y]^2)*D[u[x, y], {x, 2}] - 2*D[u[x, y], x]*D[u[x, y], y]*D[u[x, y], x, y] + (1 + D[u[x, y], x]^2)*D[u[x, y], {y, 2}] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, u[x, y], {x, y}], 60*10]];
Failed
Maple ✓
restart; pde :=(1+diff(u(x,y),y)^2)* diff(u(x,y),x$2)-2* diff(u(x,y),x)* diff(u(x,y),y)*diff(u(x,y),x,y)+ (1+diff(u(x,y),x)^2)*diff(u(x,y),y$2)=0; cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,u(x,y))),output='realtime'));
\[u \left ( x,y \right ) ={\it \_C7}\, \left ( \tanh \left ( \left ( x-iy \right ) {\it \_C2}+{\it \_C1} \right ) \right ) ^{3}+{\it \_C5}\,\tanh \left ( \left ( x-iy \right ) {\it \_C2}+{\it \_C1} \right ) +{\it \_C4}\]
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