Added June 2, 2019.
Problem 3.3(e) nonlinear pde’s by Lokenath Debnath, 3rd edition.
Solve for \(u(x,y)\) \[ 2 x y u_x+(x^2+y^2)u_y=0 \]
Mathematica ✓
ClearAll["Global`*"]; pde = 2*x*y*D[u[x, y], x] + (x^2+y^2)*D[u[x, y], y] ==0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde ,u[x, y], {x, y}], 60*10]];
\[\left \{\left \{u(x,y)\to c_1\left (\frac {y^2}{x}-x\right )\right \}\right \}\]
Maple ✓
restart; pde :=2*x*y*diff(u(x,y),x)+(x^2+y^2)*diff(u(x,y),y)=0; cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,u(x,y))),output='realtime'));
\[u \left ( x,y \right ) ={\it \_F1} \left ( {\frac {-{x}^{2}+{y}^{2}}{x}} \right ) \]
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