\[ y'(x)=\frac {(x-y(x)) y(x) (y(x)+1)}{x (x y(x)-y(x)+x)} \] ✓ Mathematica : cpu = 21.2753 (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 = 0.345 (sec), leaf count = 73
\[ \left \{ y \left ( x \right ) =-{x{{\rm e}^{{\it RootOf} \left ( -\ln \left ( {\frac {{{\rm e}^{{\it \_Z}}}}{2}}+{\frac {9}{2}} \right ) {{\rm e}^{{\it \_Z}}}+3\,{\it \_C1}\,{{\rm e}^{{\it \_Z}}}+{\it \_Z}\,{{\rm e}^{{\it \_Z}}}-{{\rm e}^{{\it \_Z}}}x+9 \right ) }} \left ( -9+ \left ( x-1 \right ) {{\rm e}^{{\it RootOf} \left ( -\ln \left ( {\frac {{{\rm e}^{{\it \_Z}}}}{2}}+{\frac {9}{2}} \right ) {{\rm e}^{{\it \_Z}}}+3\,{\it \_C1}\,{{\rm e}^{{\it \_Z}}}+{\it \_Z}\,{{\rm e}^{{\it \_Z}}}-{{\rm e}^{{\it \_Z}}}x+9 \right ) }} \right ) ^{-1}} \right \} \]