\[ y'(x)=\frac {F\left (x^3 y(x)\right )-3 x^2 y(x)}{x^3} \] ✓ Mathematica : cpu = 0.261613 (sec), leaf count = 117
\[\text {Solve}\left [\int _1^{y(x)}-\frac {x^3+F\left (x^3 K[2]\right ) \int _1^x\left (\frac {3 K[1]^5 K[2] F'\left (K[1]^3 K[2]\right )}{F\left (K[1]^3 K[2]\right )^2}-\frac {3 K[1]^2}{F\left (K[1]^3 K[2]\right )}\right )dK[1]}{F\left (x^3 K[2]\right )}dK[2]+\int _1^x\left (1-\frac {3 K[1]^2 y(x)}{F\left (K[1]^3 y(x)\right )}\right )dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.32 (sec), leaf count = 22
\[ \left \{ y \left ( x \right ) ={\frac {{\it RootOf} \left ( x-\int ^{{\it \_Z}}\! \left ( F \left ( {\it \_a} \right ) \right ) ^{-1}{d{\it \_a}}+{\it \_C1} \right ) }{{x}^{3}}} \right \} \]