\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {y \left ( x \right ) \left ( y \left ( x \right ) +x \right ) \left ( 1+y \left ( x \right ) \right ) }{x \left ( xy \left ( x \right ) +x+y \left ( x \right ) \right ) }}=0} \]
Mathematica: cpu = 16.574105 (sec), leaf count = 386 \[ \text {Solve}\left [-\frac {2^{2/3} \left (1-\frac {\left (\frac {x^6}{(x+1)^3}\right )^{2/3} (x+1)^2 ((x-2) y(x)+x)}{x^4 ((x+1) y(x)+x)}\right ) \left (\frac {\left (\frac {x^6}{(x+1)^3}\right )^{2/3} (x+1)^2 ((x-2) y(x)+x)}{x^4 ((x+1) y(x)+x)}+2\right ) \left (\left (1-\frac {\left (\frac {x^6}{(x+1)^3}\right )^{2/3} (x+1)^2 ((x-2) y(x)+x)}{x^4 ((x+1) y(x)+x)}\right ) \log \left (\frac {\frac {\left (\frac {x^6}{(x+1)^3}\right )^{2/3} (x+1)^2 ((x-2) y(x)+x)}{x^4 ((x+1) y(x)+x)}+2}{\sqrt [3]{2}}\right )+\left (\frac {\left (\frac {x^6}{(x+1)^3}\right )^{2/3} (x+1)^2 ((x-2) y(x)+x)}{x^4 ((x+1) y(x)+x)}-1\right ) \log \left (2^{2/3} \left (1-\frac {\left (\frac {x^6}{(x+1)^3}\right )^{2/3} (x+1)^2 ((x-2) y(x)+x)}{x^4 ((x+1) y(x)+x)}\right )\right )+3\right )}{9 \left (\frac {3 \left (\frac {x^6}{(x+1)^3}\right )^{2/3} (x+1)^2 ((x-2) y(x)+x)}{x^4 ((x+1) y(x)+x)}-\frac {((x-2) y(x)+x)^3}{((x+1) y(x)+x)^3}-2\right )}=c_1+\frac {2^{2/3} \left (\frac {x^6}{(x+1)^3}\right )^{2/3} (x+1)^2}{9 x^3},y(x)\right ] \]
Maple: cpu = 0.140 (sec), leaf count = 97 \[ \left \{ y \left ( x \right ) =-{x{{\rm e}^{{\it RootOf} \left ( -\ln \left ( {\frac {{{\rm e}^{{\it \_Z}}}}{2}}+{\frac {9}{2}} \right ) { {\rm e}^{{\it \_Z}}}+3\,{\it \_C1}\,{{\rm e}^{{\it \_Z}}}+{\it \_Z}\,{ {\rm e}^{{\it \_Z}}}+x{{\rm e}^{{\it \_Z}}}+9 \right ) }} \left ( { {\rm e}^{{\it RootOf} \left ( -\ln \left ( {\frac {{{\rm e}^{{\it \_Z}} }}{2}}+{\frac {9}{2}} \right ) {{\rm e}^{{\it \_Z}}}+3\,{\it \_C1}\,{ {\rm e}^{{\it \_Z}}}+{\it \_Z}\,{{\rm e}^{{\it \_Z}}}+x{{\rm e}^{{\it \_Z}}}+9 \right ) }}x+{{\rm e}^{{\it RootOf} \left ( -\ln \left ( { \frac {{{\rm e}^{{\it \_Z}}}}{2}}+{\frac {9}{2}} \right ) {{\rm e}^{{ \it \_Z}}}+3\,{\it \_C1}\,{{\rm e}^{{\it \_Z}}}+{\it \_Z}\,{{\rm e}^{{ \it \_Z}}}+x{{\rm e}^{{\it \_Z}}}+9 \right ) }}+9 \right ) ^{-1}} \right \} \]