Added June 3, 2019.
Problem 3.3(f) nonlinear pde’s by Lokenath Debnath, 3rd edition.
Solve for \(u(x,y)\) \[ (y+u) u_x+y u_y=x-y \]
Mathematica ✗
ClearAll["Global`*"]; pde = (y+u[x,y])*D[u[x, y], x] + y*D[u[x, y], y] ==x-y; sol = AbsoluteTiming[TimeConstrained[DSolve[pde ,u[x, y], {x, y}], 60*10]];
Failed
Maple ✓
restart; pde :=(y+u(x,y))*diff(u(x,y),x)+y*diff(u(x,y),y)=x-y; cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,u(x,y),'build')),output='realtime'));
\[u \left (x , y\right ) = \frac {-c_{1} y -y +\sqrt {c_{1}^{2} x^{2}+y^{2}+c_{1} \left (2 x y +2 c_{2}\right )}}{c_{1}}\]
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