Added June 3, 2019.
Problem 3.4 nonlinear pde’s by Lokenath Debnath, 3rd edition.
Solve for \(u(x,y)\) \[ u_x+2 x y^2 u_y=0 \]
Mathematica ✓
ClearAll["Global`*"]; pde = D[u[x, y], x] + 2*x*y^2*D[u[x,y],y] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde ,u[x, y], {x, y}], 60*10]];
\[\left \{\left \{u(x,y)\to c_1\left (-\frac {x^2 y+1}{y}\right )\right \}\right \}\]
Maple ✓
restart; pde := diff(u(x,y),x)+ 2*x*y^2*diff(u(x,y),y)= 0; cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,u(x,y))),output='realtime'));
\[u \left ( x,y \right ) ={\it \_F1} \left ( {\frac {y{x}^{2}+1}{y}} \right ) \]
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