Taken from Mathematica DSolve help pages
Another example of nonlinear Clairaut equation
Solve for \(u(x,y)\) \[ u = x u_x+ y u_y + \sin ( u_x + u_y ) \]
Mathematica ✓
ClearAll["Global`*"]; pde = u[x, y] == x*D[u[x, y], x] + y*D[u[x, y], y] + Sin[D[u[x, y], x] + D[u[x, y], y]]; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, u[x, y], {x, y}], 60*10]];
\[\{\{u(x,y)\to c_1 x+c_2 y+\sin (c_1+c_2)\}\}\]
Maple ✓
restart; pde := u(x,y)= x*diff(u(x,y),x)+y*diff(u(x,y),y)+sin(diff(u(x,y),x)+diff(u(x,y),y)); cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,u(x,y))),output='realtime'));
\[u \left ( x,y \right ) =x{\it \_c}_{{1}}+y{\it \_c}_{{2}}+\sin \left ( {\it \_c}_{{1}}+{\it \_c}_{{2}} \right ) \]
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