Added June 3, 2019.
Problem 3.8(b) nonlinear pde’s by Lokenath Debnath, 3rd edition.
Solve for \(u(x,y,z)\) \[ x^2 u_x+y^2 u_y+z(x+y)u_z=0 \]
Mathematica ✓
ClearAll["Global`*"]; pde = x^2*D[u[x, y,z], x] +y^2*D[u[x, y,z], y]+z*(x+y)*D[u[x, y,z], z]== 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde ,u[x, y,z], {x, y,z}], 60*10]];
\[\left \{\left \{u(x,y,z)\to c_1\left (\frac {1}{x}-\frac {1}{y},\frac {z}{x y}\right )\right \}\right \}\]
Maple ✓
restart; pde :=x^2*diff(u(x,y,z),x)+y^2*diff(u(x,y,z),y)+z*(x+y)*diff(u(x,y,z),z)= 0; cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,u(x,y,z))),output='realtime'));
\[u \left (x , y , z\right ) = \textit {\_F1} \left (\frac {x -y}{x y}, \frac {z}{x y}\right )\]
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