\[ y''(x)=\frac {x y(x)}{x^3+1}-\frac {\left (x^3-1\right ) y'(x)}{x \left (x^3+1\right )} \] ✓ Mathematica : cpu = 0.13121 (sec), leaf count = 57
\[\left \{\left \{y(x)\to -\frac {1}{2} c_2 \sqrt [3]{x^3+1} x^2 \, _2F_1\left (\frac {1}{3},\frac {2}{3};\frac {5}{3};-x^3\right )+c_1 \sqrt [3]{x^3+1}+c_2 x^2\right \}\right \}\]
✓ Maple : cpu = 0.142 (sec), leaf count = 30
\[ \left \{ y \left ( x \right ) =\sqrt [3]{{x}^{3}+1} \left ( {\mbox {$_2$F$_1$}({\frac {2}{3}},{\frac {4}{3}};\,{\frac {5}{3}};\,-{x}^{3})}{\it \_C1}\,{x}^{2}+{\it \_C2} \right ) \right \} \]