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'));
\[u \left ( x,y \right ) ={\it \_C1}\,x-x-{\frac {1}{ \left ( {\it \_C1}\,x+y \right ) ^{2}} \left ( {\frac { \left ( -1/2+i/2\sqrt {3} \right ) ^{6}}{64\,{{\it \_C2}}^{3}} \left ( -2\,{\frac { \left ( {\it \_C1}\,x+y \right ) {\it \_C2}}{{\it \_C1}+1}\sqrt [3]{ \left ( 4+4\,\sqrt {{\frac {4\, \left ( {\it \_C1}\,x+y \right ) ^{3}{{\it \_C2}}^{3}+{\it \_C1}+1}{{\it \_C1}+1}}} \right ) \left ( {\it \_C1}+1 \right ) ^{2}}}+8\,{ \left ( {\it \_C1}\,x+y \right ) ^{2}{{\it \_C2}}^{2}{\frac {1}{\sqrt [3]{ \left ( 4+4\,\sqrt {{\frac {4\, \left ( {\it \_C1}\,x+y \right ) ^{3}{{\it \_C2}}^{3}+{\it \_C1}+1}{{\it \_C1}+1}}} \right ) \left ( {\it \_C1}+1 \right ) ^{2}}}}}+4\,i\sqrt {3} \left ( 1/2\,{\frac { \left ( {\it \_C1}\,x+y \right ) {\it \_C2}}{{\it \_C1}+1}\sqrt [3]{ \left ( 4+4\,\sqrt {{\frac {4\, \left ( {\it \_C1}\,x+y \right ) ^{3}{{\it \_C2}}^{3}+{\it \_C1}+1}{{\it \_C1}+1}}} \right ) \left ( {\it \_C1}+1 \right ) ^{2}}}+2\,{ \left ( {\it \_C1}\,x+y \right ) ^{2}{{\it \_C2}}^{2}{\frac {1}{\sqrt [3]{ \left ( 4+4\,\sqrt {{\frac {4\, \left ( {\it \_C1}\,x+y \right ) ^{3}{{\it \_C2}}^{3}+{\it \_C1}+1}{{\it \_C1}+1}}} \right ) \left ( {\it \_C1}+1 \right ) ^{2}}}}} \right ) \right ) ^{2}}+ \left ( {\it \_C1}\,x+y \right ) ^{3} \right ) }\]
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