\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {xy \left ( x \right ) +x+ \left ( y \left ( x \right ) \right ) ^{2}}{ \left ( x-1 \right ) \left ( y \left ( x \right ) +x \right ) }}=0} \]
Mathematica: cpu = 0.053007 (sec), leaf count = 61 \[ \text {Solve}\left [\frac {1}{2} \log \left (\frac {y(x)^2}{x^2}+\frac {y(x)}{x}+1\right )+\frac {\tan ^{-1}\left (\frac {\frac {2 y(x)}{x}+1}{\sqrt {3}}\right )}{\sqrt {3}}=c_1+\log (1-x)-\log (x),y(x)\right ] \]
Maple: cpu = 0.218 (sec), leaf count = 48 \[ \left \{ y \left ( x \right ) ={\frac {\sqrt {3}x}{2}\tan \left ( {\it RootOf} \left ( -\sqrt {3}\ln \left ( {\frac {3\,{x}^{2} \left ( \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}+1 \right ) }{4\, \left ( x-1 \right ) ^{2}}} \right ) +2\,\sqrt {3}{\it \_C1}-2\,{\it \_Z } \right ) \right ) }-{\frac {x}{2}} \right \} \]