\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {y \left ( x \right ) \left ( 1+y \left ( x \right ) \right ) }{x \left ( -y \left ( x \right ) -1+xy \left ( x \right ) \right ) }}=0} \]
Mathematica: cpu = 0.977124 (sec), leaf count = 70 \[ \text {Solve}\left [-\frac {2^{2/3} \left (x y(x) \left (\log \left (\frac {x y(x)}{(x-1) y(x)-1}\right )-\log \left (\frac {y(x)+1}{-x y(x)+y(x)+1}\right )-\log (x)-1+\log (2)\right )+1\right )}{9 x y(x)}=c_1,y(x)\right ] \]
Maple: cpu = 0.062 (sec), leaf count = 26 \[ \left \{ y \left ( x \right ) =- \left ( x{\it lambertW} \left ( {\frac {1 }{x{\it \_C1}\,{{\rm e}^{{x}^{-1}}}}} \right ) +1 \right ) ^{-1} \right \} \]