\[ y''(x)=-\frac {27 x y(x)}{16 \left (x^3-1\right )^2} \] ✓ Mathematica : cpu = 1.68214 (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 = 0.163 (sec), leaf count = 44
\[\left \{y \left (x \right ) = \left (x^{3}-1\right )^{\frac {1}{4}} \left (c_{1} \LegendreP \left (-\frac {1}{6}, \frac {1}{3}, \sqrt {-x^{3}+1}\right )+c_{2} \LegendreQ \left (-\frac {1}{6}, \frac {1}{3}, \sqrt {-x^{3}+1}\right )\right ) \sqrt {x}\right \}\]