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]];
Failed
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'));
\[u \left ( x,y \right ) ={\frac {1}{ \left ( {\it \_C1}\,x+y \right ) ^{2}} \left ( - \left ( {{\rm e}^{{\frac {{\it \_C1}\,{\it \_C2}}{y}}}} \right ) ^{3} \left ( \RootOf \left ( \left ( \left ( {{\rm e}^{{\frac {{\it \_C1}\,{\it \_C2}}{y}}}} \right ) ^{3}{\it \_C1}+ \left ( {{\rm e}^{{\frac {{\it \_C1}\,{\it \_C2}}{y}}}} \right ) ^{3} \right ) {{\it \_Z}}^{9}+ \left ( 3\,{{\it \_C1}}^{3}{x}^{3}+9\,{{\it \_C1}}^{2}{x}^{2}y+9\,{\it \_C1}\,x{y}^{2}+3\,{y}^{3} \right ) {{\it \_Z}}^{3}-{{\it \_C1}}^{3}{x}^{3}-3\,{{\it \_C1}}^{2}{x}^{2}y-3\,{\it \_C1}\,x{y}^{2}-{y}^{3} \right ) \right ) ^{6}- \left ( x+y \right ) \left ( {\it \_C1}\,x+y \right ) ^{2} \right ) }\]
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