Added June 3, 2019.
Problem 3.17(a) nonlinear pde’s by Lokenath Debnath, 3rd edition.
Solve for \(u(x,y)\) \[ (y+u)u_x+(x+u)u_y=x+y \]
Mathematica ✗
ClearAll["Global`*"]; pde = (y+u[x,y])*D[u[x, y], x] +(x+u[x,y])*D[u[x, y], y]== x+y; sol = AbsoluteTiming[TimeConstrained[DSolve[pde ,u[x, y], {x, y}], 60*10]];
$Aborted
Maple ✓
restart; pde :=(y+u(x,y))*diff(u(x,y),x) + (x+u(x,y))*diff(u(x,y),y)=x+y; cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,u(x,y),'build') ),output='realtime'));
\[u \left (x , y\right ) = \frac {-\RootOf \left (\left (c_{1} {\mathrm e}^{\frac {3 c_{1} c_{2}}{y}}+{\mathrm e}^{\frac {3 c_{1} c_{2}}{y}}\right ) \mathit {\_Z}^{9}-c_{1}^{3} x^{3}-3 c_{1}^{2} x^{2} y -3 c_{1} x y^{2}+\left (3 c_{1}^{3} x^{3}+9 c_{1}^{2} x^{2} y +9 c_{1} x y^{2}+3 y^{3}\right ) \mathit {\_Z}^{3}-y^{3}\right )^{6} {\mathrm e}^{\frac {3 c_{1} c_{2}}{y}}-\left (x +y \right ) \left (c_{1} x +y \right )^{2}}{\left (c_{1} x +y \right )^{2}}\]
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