\[ y'(x)=\frac {y(x) \left (x^2 y(x)+x^3+y(x)^2\right )}{(x-1) x^2 (y(x)+x)} \] ✓ Mathematica : cpu = 0.194395 (sec), leaf count = 68
\[\text {Solve}\left [-\frac {1}{2} \log \left (\frac {y(x)^2}{x^2}+\frac {y(x)}{x}+1\right )+\log \left (\frac {y(x)}{x}\right )+\frac {\tan ^{-1}\left (\frac {\frac {2 y(x)}{x}+1}{\sqrt {3}}\right )}{\sqrt {3}}=\log (1-x)-\log (x)+c_1,y(x)\right ]\] ✓ Maple : cpu = 1.25 (sec), leaf count = 61
\[ \left \{ -{\frac {1}{2}\ln \left ( {\frac { \left ( y \left ( x \right ) \right ) ^{2}+xy \left ( x \right ) +{x}^{2}}{{x}^{2}}} \right ) }+{\frac {\sqrt {3}}{3}\arctan \left ( {\frac { \left ( x+2\,y \left ( x \right ) \right ) \sqrt {3}}{3\,x}} \right ) }+\ln \left ( {\frac {y \left ( x \right ) }{x}} \right ) -\ln \left ( x-1 \right ) +\ln \left ( x \right ) -{\it \_C1}=0 \right \} \]