Added June 3, 2019.
Problem 3.8(a) nonlinear pde’s by Lokenath Debnath, 3rd edition.
Solve for \(u(x,y,z)\) \[ x u_x+y u_y+z u_z=0 \]
Mathematica ✓
ClearAll["Global`*"]; pde = x*D[u[x, y,z], x] +y*D[u[x, y,z], y]+z*D[u[x, y,z], z]== 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde ,u[x, y,z], {x, y,z}], 60*10]];
\[\left \{\left \{u(x,y,z)\to c_1\left (\frac {y}{x},\frac {z}{x}\right )\right \}\right \}\]
Maple ✓
restart; pde :=x*diff(u(x,y,z),x)+diff(u(x,y,z),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'));
\[u \left ( x,y,z \right ) ={\it \_F1} \left ( -\ln \left ( x \right ) +y,-\ln \left ( x \right ) +z \right ) \]
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