\[ 8 \left (1-x^3\right ) y(x) y''(x)-4 \left (1-x^3\right ) y'(x)^2-12 x^2 y(x) y'(x)+3 x y(x)^2=0 \] ✓ Mathematica : cpu = 2832.24 (sec), leaf count = 134
\[\left \{\left \{y(x)\to c_2 \exp \left (\int _1^x -\frac {2 \left (-\frac {3}{32} c_1 K[1]^2 \, _2F_1\left (\frac {11}{12},\frac {5}{4};\frac {5}{3};K[1]^3\right )+\frac {21}{64} \sqrt [3]{-1} K[1]^3 \, _2F_1\left (\frac {5}{4},\frac {19}{12};\frac {7}{3};K[1]^3\right )+\sqrt [3]{-1} \, _2F_1\left (\frac {1}{4},\frac {7}{12};\frac {4}{3};K[1]^3\right )\right )}{-c_1 \, _2F_1\left (-\frac {1}{12},\frac {1}{4};\frac {2}{3};K[1]^3\right )-\sqrt [3]{-1} K[1] \, _2F_1\left (\frac {1}{4},\frac {7}{12};\frac {4}{3};K[1]^3\right )} \, dK[1]\right )\right \}\right \}\] ✓ Maple : cpu = 0.362 (sec), leaf count = 49
\[ \left \{ y \left ( x \right ) ={\frac {x}{{\it \_C1}} \left ( {\it \_C1}\,{\it LegendreQ} \left ( -{\frac {1}{6}},{\frac {1}{3}},\sqrt {- \left ( x-1 \right ) \left ( {x}^{2}+x+1 \right ) } \right ) +{\frac {{\it \_C2}}{2}{\it LegendreP} \left ( -{\frac {1}{6}},{\frac {1}{3}},\sqrt {- \left ( x-1 \right ) \left ( {x}^{2}+x+1 \right ) } \right ) } \right ) ^{2}} \right \} \]