\[ y''(x)=-\frac {27 x y(x)}{16 \left (x^3-1\right )^2} \] ✓ Mathematica : cpu = 300.211 (sec), leaf count = 81
\[\left \{\left \{y(x)\to \frac {c_1 \sqrt [3]{x^3} \sqrt [4]{x^3-1} \, _2F_1\left (-\frac {1}{12},\frac {1}{4};\frac {2}{3};x^3\right )}{x}+\frac {\sqrt [3]{-1} c_2 \left (x^3\right )^{2/3} \sqrt [4]{x^3-1} \, _2F_1\left (\frac {1}{4},\frac {7}{12};\frac {4}{3};x^3\right )}{x}\right \}\right \}\] ✓ Maple : cpu = 0.231 (sec), leaf count = 44
\[ \left \{ y \left ( x \right ) =\sqrt {x}\sqrt [4]{{x}^{3}-1} \left ( {\it LegendreP} \left ( -{\frac {1}{6}},{\frac {1}{3}},\sqrt {-{x}^{3}+1} \right ) {\it \_C1}+{\it LegendreQ} \left ( -{\frac {1}{6}},{\frac {1}{3}},\sqrt {-{x}^{3}+1} \right ) {\it \_C2} \right ) \right \} \]