\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {{x}^{3}y \left ( x \right ) +{x}^{3}+x \left ( y \left ( x \right ) \right ) ^{2}+ \left ( y \left ( x \right ) \right ) ^{3}}{ \left ( x-1 \right ) {x}^{3}}}=0} \]
Mathematica: cpu = 0.028504 (sec), leaf count = 57 \[ \text {Solve}\left [-\frac {1}{4} \log \left (\frac {y(x)^2}{x^2}+1\right )+\frac {1}{2} \log \left (\frac {y(x)}{x}+1\right )+\frac {1}{2} \tan ^{-1}\left (\frac {y(x)}{x}\right )=c_1+\log (1-x)-\log (x),y(x)\right ] \]
Maple: cpu = 0.078 (sec), leaf count = 50 \[ \left \{ {\frac {1}{2}\ln \left ( {\frac {y \left ( x \right ) +x}{x}} \right ) }-{\frac {1}{4}\ln \left ( {\frac { \left ( y \left ( x \right ) \right ) ^{2}+{x}^{2}}{{x}^{2}}} \right ) }+{\frac {1}{2} \arctan \left ( {\frac {y \left ( x \right ) }{x}} \right ) }+\ln \left ( x \right ) -\ln \left ( x-1 \right ) -{\it \_C1}=0 \right \} \]