\[ a y(x)^2+b x+c+y(x)^2 y'(x)^2+2 x y(x) y'(x)=0 \] ✗ Mathematica : cpu = 300.229 (sec), leaf count = 0 , timed out
$Aborted
✓ Maple : cpu = 2.316 (sec), leaf count = 551
\[\left \{y \left (x \right ) = -\frac {\sqrt {16}\, \sqrt {\left (\left (-\frac {b x}{4}-\frac {c}{4}\right ) a^{2}+\left (a x -\frac {1}{2} b +x \right )^{2} \left (a +1\right )^{2} a \RootOf \left (2 c_{1} a +2 \left (\int _{}^{\textit {\_Z}}\frac {\left (-4 \textit {\_a} \,a^{2}+\sqrt {-\left (4 \textit {\_a} \,a^{3}+8 \textit {\_a} \,a^{2}+4 \textit {\_a} a -1\right ) {\mathrm e}^{\frac {4 a +4}{b}}}\, {\mathrm e}^{-\frac {2 \left (a +1\right )}{b}}-8 \textit {\_a} a -4 \textit {\_a} -1\right ) b}{4 \textit {\_a} \left (4 \textit {\_a} \,a^{2}+8 \textit {\_a} a +4 \textit {\_a} +a +2\right ) \left (a +1\right )}d \textit {\_a} \right ) a -b \ln \left (2 a x -b +2 x \right )+2 c_{1}+2 \left (\int _{}^{\textit {\_Z}}\frac {\left (-4 \textit {\_a} \,a^{2}+\sqrt {-\left (4 \textit {\_a} \,a^{3}+8 \textit {\_a} \,a^{2}+4 \textit {\_a} a -1\right ) {\mathrm e}^{\frac {4 a +4}{b}}}\, {\mathrm e}^{-\frac {2 \left (a +1\right )}{b}}-8 \textit {\_a} a -4 \textit {\_a} -1\right ) b}{4 \textit {\_a} \left (4 \textit {\_a} \,a^{2}+8 \textit {\_a} a +4 \textit {\_a} +a +2\right ) \left (a +1\right )}d \textit {\_a} \right )\right )-\frac {b^{2}}{16}+\left (-\frac {b x}{4}-\frac {c}{2}\right ) a -\frac {c}{4}\right ) a}}{2 \left (a +1\right ) a}, y \left (x \right ) = \frac {\sqrt {16}\, \sqrt {\left (\left (-\frac {b x}{4}-\frac {c}{4}\right ) a^{2}+\left (a x -\frac {1}{2} b +x \right )^{2} \left (a +1\right )^{2} a \RootOf \left (2 c_{1} a +2 \left (\int _{}^{\textit {\_Z}}\frac {\left (-4 \textit {\_a} \,a^{2}+\sqrt {-\left (4 \textit {\_a} \,a^{3}+8 \textit {\_a} \,a^{2}+4 \textit {\_a} a -1\right ) {\mathrm e}^{\frac {4 a +4}{b}}}\, {\mathrm e}^{-\frac {2 \left (a +1\right )}{b}}-8 \textit {\_a} a -4 \textit {\_a} -1\right ) b}{4 \textit {\_a} \left (4 \textit {\_a} \,a^{2}+8 \textit {\_a} a +4 \textit {\_a} +a +2\right ) \left (a +1\right )}d \textit {\_a} \right ) a -b \ln \left (2 a x -b +2 x \right )+2 c_{1}+2 \left (\int _{}^{\textit {\_Z}}\frac {\left (-4 \textit {\_a} \,a^{2}+\sqrt {-\left (4 \textit {\_a} \,a^{3}+8 \textit {\_a} \,a^{2}+4 \textit {\_a} a -1\right ) {\mathrm e}^{\frac {4 a +4}{b}}}\, {\mathrm e}^{-\frac {2 \left (a +1\right )}{b}}-8 \textit {\_a} a -4 \textit {\_a} -1\right ) b}{4 \textit {\_a} \left (4 \textit {\_a} \,a^{2}+8 \textit {\_a} a +4 \textit {\_a} +a +2\right ) \left (a +1\right )}d \textit {\_a} \right )\right )-\frac {b^{2}}{16}+\left (-\frac {b x}{4}-\frac {c}{2}\right ) a -\frac {c}{4}\right ) a}}{2 \left (a +1\right ) a}\right \}\]