ODE
\[ 8 \left (1-x^3\right ) y(x) y''(x)+4 \left (1-x^3\right ) y'(x)^2-12 x^2 y(x) y'(x)+3 x y(x)^2=0 \] ODE Classification
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]]
Book solution method
TO DO
Mathematica ✗
cpu = 599.998 (sec), leaf count = 0 , timed out
$Aborted
Maple ✓
cpu = 0.797 (sec), leaf count = 162
\[ \left \{ \left ( \left ( y \left ( x \right ) \right ) ^{{\frac {3}{2}}} \left ( -1+x \right ) \left ( {x}^{2}+x+1 \right ) \left ( \sqrt {10}+1 \right ) {\it LegendreQ} \left ( {\frac {1}{2}}+{\frac {\sqrt {10}}{6}},{\frac {1}{3}},\sqrt {-{x}^{3}+1} \right ) +{\it \_C1}\,\sqrt {x}\sqrt {-{x}^{3}+1}\sqrt {{x}^{3}-1} \right ) {\it LegendreP} \left ( -{\frac {1}{2}}+{\frac {\sqrt {10}}{6}},{\frac {1}{3}},\sqrt {-{x}^{3}+1} \right ) - \left ( \left ( y \left ( x \right ) \right ) ^{{\frac {3}{2}}} \left ( -1+x \right ) \left ( {x}^{2}+x+1 \right ) \left ( \sqrt {10}+1 \right ) {\it LegendreP} \left ( {\frac {1}{2}}+{\frac {\sqrt {10}}{6}},{\frac {1}{3}},\sqrt {-{x}^{3}+1} \right ) -{\it \_C2}\,\sqrt {{x}^{3}-1}\sqrt {-{x}^{3}+1}\sqrt {x} \right ) {\it LegendreQ} \left ( -{\frac {1}{2}}+{\frac {\sqrt {10}}{6}},{\frac {1}{3}},\sqrt {-{x}^{3}+1} \right ) =0 \right \} \] Mathematica raw input
DSolve[3*x*y[x]^2 - 12*x^2*y[x]*y'[x] + 4*(1 - x^3)*y'[x]^2 + 8*(1 - x^3)*y[x]*y''[x] == 0,y[x],x]
Mathematica raw output
$Aborted
Maple raw input
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),'implicit')
Maple raw output
(y(x)^(3/2)*(-1+x)*(x^2+x+1)*(10^(1/2)+1)*LegendreQ(1/2+1/6*10^(1/2),1/3,(-x^3+1)^(1/2))+_C1*x^(1/2)*(-x^3+1)^(1/2)*(x^3-1)^(1/2))*LegendreP(-1/2+1/6*10^(1/2),1/3,(-x^3+1)^(1/2))-(y(x)^(3/2)*(-1+x)*(x^2+x+1)*(10^(1/2)+1)*LegendreP(1/2+1/6*10^(1/2),1/3,(-x^3+1)^(1/2))-_C2*(x^3-1)^(1/2)*(-x^3+1)^(1/2)*x^(1/2))*LegendreQ(-1/2+1/6*10^(1/2),1/3,(-x^3+1)^(1/2)) = 0