\[ a y(x)^2+b x+c+y(x)^2 y'(x)^2+2 x y(x) y'(x)=0 \] ✗ Mathematica : cpu = 3602.89 (sec), leaf count = 0 , timed out
$Aborted
✓ Maple : cpu = 8.711 (sec), leaf count = 551
\[ \left \{ y \left ( x \right ) =-{\frac {\sqrt {16}}{2\,a \left ( a+1 \right ) }\sqrt {a \left ( a \left ( a+1 \right ) ^{2} \left ( ax-{\frac {b}{2}}+x \right ) ^{2}{\it RootOf} \left ( -b\ln \left ( 2\,ax-b+2\,x \right ) +2\,\int ^{{\it \_Z}}\!1/4\,{\frac {b}{ \left ( a+1 \right ) \left ( 4\,{\it \_a}\,{a}^{2}+8\,a{\it \_a}+4\,{\it \_a}+a+2 \right ) {\it \_a}} \left ( -4\,{\it \_a}\,{a}^{2}+\sqrt {-{{\rm e}^{4\,{\frac {a+1}{b}}}} \left ( 4\,{\it \_a}\,{a}^{3}+8\,{\it \_a}\,{a}^{2}+4\,a{\it \_a}-1 \right ) }{{\rm e}^{-2\,{\frac {a+1}{b}}}}-8\,a{\it \_a}-4\,{\it \_a}-1 \right ) }{d{\it \_a}}a+2\,{\it \_C1}\,a+2\,\int ^{{\it \_Z}}\!1/4\,{\frac {b}{ \left ( a+1 \right ) \left ( 4\,{\it \_a}\,{a}^{2}+8\,a{\it \_a}+4\,{\it \_a}+a+2 \right ) {\it \_a}} \left ( -4\,{\it \_a}\,{a}^{2}+\sqrt {-{{\rm e}^{4\,{\frac {a+1}{b}}}} \left ( 4\,{\it \_a}\,{a}^{3}+8\,{\it \_a}\,{a}^{2}+4\,a{\it \_a}-1 \right ) }{{\rm e}^{-2\,{\frac {a+1}{b}}}}-8\,a{\it \_a}-4\,{\it \_a}-1 \right ) }{d{\it \_a}}+2\,{\it \_C1} \right ) + \left ( -{\frac {bx}{4}}-{\frac {c}{4}} \right ) {a}^{2}+ \left ( -{\frac {bx}{4}}-{\frac {c}{2}} \right ) a-{\frac {{b}^{2}}{16}}-{\frac {c}{4}} \right ) }},y \left ( x \right ) ={\frac {\sqrt {16}}{2\,a \left ( a+1 \right ) }\sqrt {a \left ( a \left ( a+1 \right ) ^{2} \left ( ax-{\frac {b}{2}}+x \right ) ^{2}{\it RootOf} \left ( -b\ln \left ( 2\,ax-b+2\,x \right ) +2\,\int ^{{\it \_Z}}\!1/4\,{\frac {b}{ \left ( a+1 \right ) \left ( 4\,{\it \_a}\,{a}^{2}+8\,a{\it \_a}+4\,{\it \_a}+a+2 \right ) {\it \_a}} \left ( -4\,{\it \_a}\,{a}^{2}+\sqrt {-{{\rm e}^{4\,{\frac {a+1}{b}}}} \left ( 4\,{\it \_a}\,{a}^{3}+8\,{\it \_a}\,{a}^{2}+4\,a{\it \_a}-1 \right ) }{{\rm e}^{-2\,{\frac {a+1}{b}}}}-8\,a{\it \_a}-4\,{\it \_a}-1 \right ) }{d{\it \_a}}a+2\,{\it \_C1}\,a+2\,\int ^{{\it \_Z}}\!1/4\,{\frac {b}{ \left ( a+1 \right ) \left ( 4\,{\it \_a}\,{a}^{2}+8\,a{\it \_a}+4\,{\it \_a}+a+2 \right ) {\it \_a}} \left ( -4\,{\it \_a}\,{a}^{2}+\sqrt {-{{\rm e}^{4\,{\frac {a+1}{b}}}} \left ( 4\,{\it \_a}\,{a}^{3}+8\,{\it \_a}\,{a}^{2}+4\,a{\it \_a}-1 \right ) }{{\rm e}^{-2\,{\frac {a+1}{b}}}}-8\,a{\it \_a}-4\,{\it \_a}-1 \right ) }{d{\it \_a}}+2\,{\it \_C1} \right ) + \left ( -{\frac {bx}{4}}-{\frac {c}{4}} \right ) {a}^{2}+ \left ( -{\frac {bx}{4}}-{\frac {c}{2}} \right ) a-{\frac {{b}^{2}}{16}}-{\frac {c}{4}} \right ) }} \right \} \]