\[ y'(x)=\frac {F\left (x^3 y(x)\right )-3 x^2 y(x)}{x^3} \] ✓ Mathematica : cpu = 62.7832 (sec), leaf count = 107
\[\text {Solve}\left [c_1=\int _1^{y(x)} \left (-\int _1^x \frac {3 K[1]^5 K[2] F'\left (K[1]^3 K[2]\right )-3 K[1]^2 F\left (K[1]^3 K[2]\right )}{F\left (K[1]^3 K[2]\right )^2} \, dK[1]-\frac {x^3}{F\left (x^3 K[2]\right )}\right ) \, dK[2]+\int _1^x \left (1-\frac {3 y(x) K[1]^2}{F\left (y(x) K[1]^3\right )}\right ) \, dK[1],y(x)\right ]\]
✓ Maple : cpu = 0.179 (sec), leaf count = 22
\[ \left \{ y \left ( x \right ) ={\frac {{\it RootOf} \left ( x-\int ^{{\it \_Z}}\! \left ( F \left ( {\it \_a} \right ) \right ) ^{-1}{d{\it \_a}}+{\it \_C1} \right ) }{{x}^{3}}} \right \} \]