\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {xy \left ( x \right ) +{x}^{3}+x \left ( y \left ( x \right ) \right ) ^{2}+ \left ( y \left ( x \right ) \right ) ^{3}}{{x}^{2}}}=0} \]
Mathematica: cpu = 0.027003 (sec), leaf count = 47 \[ \text {Solve}\left [\text {RootSum}\left [\text {$\#$1}^3+\text {$\#$1}^2+1\& ,\frac {\log \left (\frac {y(x)}{x}-\text {$\#$1}\right )}{3 \text {$\#$1}^2+2 \text {$\#$1}}\& \right ]=c_1+x,y(x)\right ] \]
Maple: cpu = 0.016 (sec), leaf count = 26 \[ \left \{ y \left ( x \right ) ={\it RootOf} \left ( -\int ^{{\it \_Z}}\! \left ( {{\it \_a}}^{3}+{{\it \_a}}^{2}+1 \right ) ^{-1}{d{\it \_a}}+x+ {\it \_C1} \right ) x \right \} \]