\[ y'(x)=\frac {F\left (x^3 y(x)\right )-3 x^2 y(x)}{x^3} \] ✓ Mathematica : cpu = 0.284743 (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 = 0.269 (sec), leaf count = 22
\[y \relax (x ) = \frac {\RootOf \left (x -\left (\int _{}^{\textit {\_Z}}\frac {1}{F \left (\textit {\_a} \right )}d \textit {\_a} \right )+c_{1}\right )}{x^{3}}\]