\[ y'(x)=\frac {y(x) (y(x)+1) (y(x)+x)}{x (x y(x)+y(x)+x)} \] ✓ Mathematica : cpu = 15.8113 (sec), leaf count = 386
\[\text {Solve}\left [\frac {2^{2/3} \left (1-\frac {\left (\frac {x^6}{(x+1)^3}\right )^{2/3} (x+1)^2 ((x-2) y(x)+x)}{x^4 ((x+1) y(x)+x)}\right ) \left (\frac {\left (\frac {x^6}{(x+1)^3}\right )^{2/3} (x+1)^2 ((x-2) y(x)+x)}{x^4 ((x+1) y(x)+x)}+2\right ) \left (\left (1-\frac {\left (\frac {x^6}{(x+1)^3}\right )^{2/3} (x+1)^2 ((x-2) y(x)+x)}{x^4 ((x+1) y(x)+x)}\right ) \log \left (2^{2/3} \left (1-\frac {\left (\frac {x^6}{(x+1)^3}\right )^{2/3} (x+1)^2 ((x-2) y(x)+x)}{x^4 ((x+1) y(x)+x)}\right )\right )+\left (\frac {\left (\frac {x^6}{(x+1)^3}\right )^{2/3} (x+1)^2 ((x-2) y(x)+x)}{x^4 ((x+1) y(x)+x)}-1\right ) \log \left (2^{2/3} \left (\frac {\left (\frac {x^6}{(x+1)^3}\right )^{2/3} (x+1)^2 ((x-2) y(x)+x)}{x^4 ((x+1) y(x)+x)}+2\right )\right )-3\right )}{9 \left (\frac {3 \left (\frac {x^6}{(x+1)^3}\right )^{2/3} (x+1)^2 ((x-2) y(x)+x)}{x^4 ((x+1) y(x)+x)}-\frac {((x-2) y(x)+x)^3}{((x+1) y(x)+x)^3}-2\right )}=\frac {2^{2/3} \left (\frac {x^6}{(x+1)^3}\right )^{2/3} (x+1)^2}{9 x^3}+c_1,y(x)\right ]\] ✓ Maple : cpu = 0.304 (sec), leaf count = 97
\[\left \{y \left (x \right ) = -\frac {x \,{\mathrm e}^{\RootOf \left (3 c_{1} {\mathrm e}^{\textit {\_Z}}+\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+x \,{\mathrm e}^{\textit {\_Z}}-{\mathrm e}^{\textit {\_Z}} \ln \left (\frac {{\mathrm e}^{\textit {\_Z}}}{2}+\frac {9}{2}\right )+9\right )}}{x \,{\mathrm e}^{\RootOf \left (3 c_{1} {\mathrm e}^{\textit {\_Z}}+\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+x \,{\mathrm e}^{\textit {\_Z}}-{\mathrm e}^{\textit {\_Z}} \ln \left (\frac {{\mathrm e}^{\textit {\_Z}}}{2}+\frac {9}{2}\right )+9\right )}+{\mathrm e}^{\RootOf \left (3 c_{1} {\mathrm e}^{\textit {\_Z}}+\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}+x \,{\mathrm e}^{\textit {\_Z}}-{\mathrm e}^{\textit {\_Z}} \ln \left (\frac {{\mathrm e}^{\textit {\_Z}}}{2}+\frac {9}{2}\right )+9\right )}+9}\right \}\]