\[ y''(x)=-\frac {27 x y(x)}{16 \left (x^3-1\right )^2} \] ✓ Mathematica : cpu = 1.55934 (sec), leaf count = 258
\[\left \{\left \{y(x)\to \frac {\sqrt {2} c_2 (1-x)^{3/4} \sqrt [4]{x^2+x+1} \int _1^x\frac {\sqrt {\sqrt {3} K[1]+\sqrt {2 K[1]-i \sqrt {3}+1} \sqrt {2 K[1]+i \sqrt {3}+1}+\sqrt {3}}}{2 (1-K[1])^{3/2} \sqrt {K[1]^2+K[1]+1}}dK[1]}{\sqrt [4]{\sqrt {3} x+\sqrt {2 x-i \sqrt {3}+1} \sqrt {2 x+i \sqrt {3}+1}+\sqrt {3}}}+\frac {\sqrt {2} c_1 (1-x)^{3/4} \sqrt [4]{x^2+x+1}}{\sqrt [4]{\sqrt {3} x+\sqrt {2 x-i \sqrt {3}+1} \sqrt {2 x+i \sqrt {3}+1}+\sqrt {3}}}\right \}\right \}\] ✓ Maple : cpu = 0.208 (sec), leaf count = 44
\[ \left \{ y \left ( x \right ) =\sqrt {x}\sqrt [4]{{x}^{3}-1} \left ( {\it LegendreQ} \left ( -{\frac {1}{6}},{\frac {1}{3}},\sqrt {-{x}^{3}+1} \right ) {\it \_C2}+{\it LegendreP} \left ( -{\frac {1}{6}},{\frac {1}{3}},\sqrt {-{x}^{3}+1} \right ) {\it \_C1} \right ) \right \} \]