\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) =-{\frac { \left ( {x}^{3}-1 \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) }{ \left ( {x}^{3}+1 \right ) x}}+{\frac {xy \left ( x \right ) }{{x}^{3}+1}}=0} \]
Mathematica: cpu = 0.131517 (sec), leaf count = 59 \[ \left \{\left \{y(x)\to \frac {1}{2} c_2 \left (2 x^2-x^2 \sqrt [3]{x^3+1} \, _2F_1\left (\frac {1}{3},\frac {2}{3};\frac {5}{3};-x^3\right )\right )+c_1 \sqrt [3]{x^3+1}\right \}\right \} \]
Maple: cpu = 0.110 (sec), leaf count = 37 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{x}^{2}\sqrt [3]{{x}^{3}+1} {\mbox {$_2$F$_1$}({\frac {2}{3}},{\frac {4}{3}};\,{\frac {5}{3}};\,-{x}^{3})} +{\it \_C2}\,\sqrt [3]{{x}^{3}+1} \right \} \]