\[ y'(x)=\frac {(x-y(x)) y(x) (y(x)+1)}{x (x y(x)-y(x)+x)} \] ✓ Mathematica : cpu = 11.1854 (sec), leaf count = 379
\[\text {Solve}\left [\frac {1}{9} 2^{2/3} \left (\frac {\left (1-\frac {(x-1)^2 \left (\frac {x^6}{(x-1)^3}\right )^{2/3} ((x+2) y(x)+x)}{x^4 ((x-1) y(x)+x)}\right ) \left (\frac {\left (\frac {x^6}{(x-1)^3}\right )^{2/3} (x-1)^2 ((x+2) y(x)+x)}{x^4 ((x-1) y(x)+x)}+2\right ) \left (\left (1-\frac {(x-1)^2 \left (\frac {x^6}{(x-1)^3}\right )^{2/3} ((x+2) y(x)+x)}{x^4 ((x-1) y(x)+x)}\right ) \log \left (2^{2/3} \left (1-\frac {(x-1)^2 \left (\frac {x^6}{(x-1)^3}\right )^{2/3} ((x+2) y(x)+x)}{x^4 ((x-1) y(x)+x)}\right )\right )+\left (\frac {(x-1)^2 \left (\frac {x^6}{(x-1)^3}\right )^{2/3} ((x+2) y(x)+x)}{x^4 ((x-1) y(x)+x)}-1\right ) \log \left (2^{2/3} \left (\frac {\left (\frac {x^6}{(x-1)^3}\right )^{2/3} (x-1)^2 ((x+2) y(x)+x)}{x^4 ((x-1) y(x)+x)}+2\right )\right )-3\right )}{\frac {3 (x-1)^2 \left (\frac {x^6}{(x-1)^3}\right )^{2/3} ((x+2) y(x)+x)}{x^4 ((x-1) y(x)+x)}-\frac {((x+2) y(x)+x)^3}{((x-1) y(x)+x)^3}-2}+\frac {\left (\frac {x^6}{(x-1)^3}\right )^{2/3} (x-1)^2}{x^3}\right )=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.224 (sec), leaf count = 73
\[y \relax (x ) = -\frac {x \,{\mathrm e}^{\RootOf \left (-\ln \left (\frac {{\mathrm e}^{\textit {\_Z}}}{2}+\frac {9}{2}\right ) {\mathrm e}^{\textit {\_Z}}+3 \,{\mathrm e}^{\textit {\_Z}} c_{1}+\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}-{\mathrm e}^{\textit {\_Z}} x +9\right )}}{-9+\left (x -1\right ) {\mathrm e}^{\RootOf \left (-\ln \left (\frac {{\mathrm e}^{\textit {\_Z}}}{2}+\frac {9}{2}\right ) {\mathrm e}^{\textit {\_Z}}+3 \,{\mathrm e}^{\textit {\_Z}} c_{1}+\textit {\_Z} \,{\mathrm e}^{\textit {\_Z}}-{\mathrm e}^{\textit {\_Z}} x +9\right )}}\]