\[ y''(x)=\frac {x y(x)}{x^3+1}-\frac {\left (x^3-1\right ) y'(x)}{x \left (x^3+1\right )} \] ✓ Mathematica : cpu = 0.247059 (sec), leaf count = 51
\[\left \{\left \{y(x)\to \frac {1}{2} c_2 \sqrt [3]{x^3+1} x^2 \, _2F_1\left (\frac {2}{3},\frac {4}{3};\frac {5}{3};-x^3\right )+c_1 \sqrt [3]{x^3+1}\right \}\right \}\] ✓ Maple : cpu = 0.101 (sec), leaf count = 30
\[y \relax (x ) = \left (x^{3}+1\right )^{\frac {1}{3}} \left (\hypergeom \left (\left [\frac {2}{3}, \frac {4}{3}\right ], \left [\frac {5}{3}\right ], -x^{3}\right ) c_{1} x^{2}+c_{2}\right )\]