\[ \boxed { 8\, \left ( -{x}^{3}+1 \right ) y \left ( x \right ) {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) -4\, \left ( -{x}^{3}+1 \right ) \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}-12\,{x}^{2}y \left ( x \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +3\,x \left ( y \left ( x \right ) \right ) ^{2}=0} \]
Mathematica: cpu = 0 (sec), leaf count = 0 \[ \text {Hanged} \]
Maple: cpu = 1.825 (sec), leaf count = 88 \[ \left \{ y \left ( x \right ) ={\frac {{{\it \_C2}}^{2}x}{4\,{\it \_C1}} \left ( {\it LegendreP} \left ( -{\frac {1}{6}},{\frac {1}{3}},\sqrt {- \left ( x-1 \right ) \left ( {x}^{2}+x+1 \right ) } \right ) \right ) ^{2 }}+{\it \_C1}\, \left ( {\it LegendreQ} \left ( -{\frac {1}{6}},{\frac { 1}{3}},\sqrt {- \left ( x-1 \right ) \left ( {x}^{2}+x+1 \right ) } \right ) \right ) ^{2}x+{\it \_C2}\,{\it LegendreP} \left ( -{\frac {1} {6}},{\frac {1}{3}},\sqrt {- \left ( x-1 \right ) \left ( {x}^{2}+x+1 \right ) } \right ) x{\it LegendreQ} \left ( -{\frac {1}{6}},{\frac {1}{ 3}},\sqrt {- \left ( x-1 \right ) \left ( {x}^{2}+x+1 \right ) } \right ) \right \} \]