\[ y''(x)=\frac {x y(x)}{x^3+1}-\frac {\left (x^3-1\right ) y'(x)}{x \left (x^3+1\right )} \] ✓ Mathematica : cpu = 0.13074 (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 = 0.158 (sec), leaf count = 37
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{x}^{2}\sqrt [3]{{x}^{3}+1}{\mbox {$_2$F$_1$}({\frac {2}{3}},{\frac {4}{3}};\,{\frac {5}{3}};\,-{x}^{3})}+{\it \_C2}\,\sqrt [3]{{x}^{3}+1} \right \} \]