Added June 3, 2019.
Problem 3.3(h) nonlinear pde’s by Lokenath Debnath, 3rd edition.
Solve for \(u(x,y)\) \[ y u_y- x u_x=1 \]
Mathematica ✓
ClearAll["Global`*"]; pde = y*D[u[x, y], y] - x*D[u[x, y], x] ==1; sol = AbsoluteTiming[TimeConstrained[DSolve[pde ,u[x, y], {x, y}], 60*10]];
\[\{\{u(x,y)\to -\log (x)+c_1(x y)\}\}\]
Maple ✓
restart; pde :=y*diff(u(x,y),y)- x*diff(u(x,y),x)=1; cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,u(x,y))),output='realtime'));
\[u \left ( x,y \right ) =-\ln \left ( x \right ) +{\it \_F1} \left ( yx \right ) \]
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