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