\[ 8 \left (1-x^3\right ) y(x) y''(x)-4 \left (1-x^3\right ) y'(x)^2-12 x^2 y(x) y'(x)+3 x y(x)^2=0 \] ✗ Mathematica : cpu = 300.004 (sec), leaf count = 0
DSolve[3*x*y[x]^2 - 12*x^2*y[x]*Derivative[1][y][x] - 4*(1 - x^3)*Derivative[1][y][x]^2 + 8*(1 - x^3)*y[x]*Derivative[2][y][x] == 0,y[x],x]
, timed out
$Aborted
✓ Maple : cpu = 0.276 (sec), leaf count = 49
dsolve(8*(-x^3+1)*y(x)*diff(diff(y(x),x),x)-4*(-x^3+1)*diff(y(x),x)^2-12*x^2*y(x)*diff(y(x),x)+3*x*y(x)^2=0,y(x))
\[y \left (x \right ) = \frac {x {\left (\operatorname {LegendreQ}\left (-\frac {1}{6}, \frac {1}{3}, \sqrt {-\left (x -1\right ) \left (x^{2}+x +1\right )}\right ) c_{1}+\frac {c_{2} \operatorname {LegendreP}\left (-\frac {1}{6}, \frac {1}{3}, \sqrt {-\left (x -1\right ) \left (x^{2}+x +1\right )}\right )}{2}\right )}^{2}}{c_{1}}\]