\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {-3\,{x}^{2}y \left ( x \right ) +F \left ( {x}^{3}y \left ( x \right ) \right ) }{{x}^{3}}}=0} \]
Mathematica: cpu = 51.408028 (sec), leaf count = 114 \[ \text {Solve}\left [\int _1^{y(x)} -\frac {F\left (x^3 K[2]\right ) \int _1^x \left (\frac {3 K[1]^5 K[2] F'\left (K[1]^3 K[2]\right )}{F\left (K[1]^3 K[2]\right )^2}-\frac {3 K[1]^2}{F\left (K[1]^3 K[2]\right )}\right ) \, dK[1]+x^3}{F\left (x^3 K[2]\right )} \, dK[2]+\int _1^x \left (1-\frac {3 y(x) K[1]^2}{F\left (y(x) K[1]^3\right )}\right ) \, dK[1]=c_1,y(x)\right ] \]
Maple: cpu = 0.140 (sec), leaf count = 22 \[ \left \{ y \left ( x \right ) ={\frac {{\it RootOf} \left ( x-\int ^{{ \it \_Z}}\! \left ( F \left ( {\it \_a} \right ) \right ) ^{-1}{d{\it \_a }}+{\it \_C1} \right ) }{{x}^{3}}} \right \} \]