\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {x \left ( -1+x-2\,xy \left ( x \right ) +2\,{x}^{3} \right ) }{{x}^{2}-y \left ( x \right ) }}=0} \]
Mathematica: cpu = 0.033504 (sec), leaf count = 36 \[ \left \{\left \{y(x)\to \frac {1}{2} \left (W\left (-e^{c_1+\frac {4 x^3}{3}-2 x^2-1}\right )+1\right )+x^2\right \}\right \} \]
Maple: cpu = 0.062 (sec), leaf count = 29 \[ \left \{ y \left ( x \right ) ={x}^{2}+{\frac {1}{2}{\it lambertW} \left ( -2\,{\frac {{{\rm e}^{4/3\,{x}^{3}}}{\it \_C1}\,{{\rm e}^{-1}} }{ \left ( {{\rm e}^{{x}^{2}}} \right ) ^{2}}} \right ) }+{\frac {1}{2}} \right \} \]