From example 3.5.4, page 212 nonlinear pde’s by Lokenath Debnath, 3rd edition.
First order PDE of three unknowns. Solve for
Mathematica ✗
ClearAll["Global`*"]; pde = (y - z)*D[u[x, y, z], x] + (z - x)*D[u[x, y, z], y] + (x - y)*D[u[x, y, z], z] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, u[x, y, z], {x, y, z}], 60*10]];
$Aborted
Maple ✓
restart; pde :=(y-z)*diff(u(x,y,z),x)+(z-x)*diff(u(x,y,z),y)+(x-y)*diff(u(x,y,z),z)=0; cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,u(x,y,z),'build')),output='realtime'));
Hand solution
Solve
We need one more equation which is
And since we know that
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