Taken from Maple pdsolve help pages, probem 5
Nonlinear first order PDE
Solve for \(f(x,y,z)\) \begin {align*} f_x + (f_y)^2 &= f(x,y,z)+z \end {align*}
Mathematica ✓
ClearAll["Global`*"]; pde = D[f[x, y, z], x] + D[f[x, y, z], y]^2 == f[x, y, z] + z; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, f[x, y, z], {x, y, z}], 60*10]];
\[\left \{\left \{f(x,y,z)\to \frac {1}{4} \left ((c_1(z)){}^2 \operatorname {ProductLog}\left (-\frac {\exp \left (\frac {(x-1) c_1(z)+c_2(z)+y}{c_1(z)}\right )}{c_1(z)}\right ){}^2+2 (c_1(z)){}^2 \operatorname {ProductLog}\left (-\frac {\exp \left (\frac {(x-1) c_1(z)+c_2(z)+y}{c_1(z)}\right )}{c_1(z)}\right )-4 z\right )\right \}\right \}\]
Maple ✓
restart; pde := diff(f(x,y,z),x) + (diff(f(x,y,z),y))^2 = f(x,y,z)+z; cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,f(x,y,z),'build')),output='realtime'));
\[f \left (x , y , z\right ) = \frac {\left (-c_{5}^{2} z \,{\mathrm e}^{-x}-c_{3}^{2} {\mathrm e}^{x}-c_{5} \left (c_{3} y +c_{4} z +c_{1}\right )\right ) {\mathrm e}^{x}}{c_{5}^{2}}\]
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