\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {1}{x} \left ( 2\,y \left ( x \right ) +F \left ( {\frac {y \left ( x \right ) }{{x}^{2}}} \right ) {x}^{3} \right ) }=0} \]
Mathematica: cpu = 739.416394 (sec), leaf count = 118 \[ \text {Solve}\left [\int _1^{y(x)} -\frac {x^2 F\left (\frac {K[2]}{x^2}\right ) \left (\int _1^x \left (\frac {2}{K[1]^3 F\left (\frac {K[2]}{K[1]^2}\right )}-\frac {2 K[2] F'\left (\frac {K[2]}{K[1]^2}\right )}{K[1]^5 F\left (\frac {K[2]}{K[1]^2}\right )^2}\right ) \, dK[1]\right )+1}{x^2 F\left (\frac {K[2]}{x^2}\right )} \, dK[2]+\int _1^x \left (\frac {2 y(x)}{K[1]^3 F\left (\frac {y(x)}{K[1]^2}\right )}+1\right ) \, dK[1]=c_1,y(x)\right ] \]
Maple: cpu = 0.078 (sec), leaf count = 22 \[ \left \{ y \left ( x \right ) ={\it RootOf} \left ( -x+\int ^{{\it \_Z}} \! \left ( F \left ( {\it \_a} \right ) \right ) ^{-1}{d{\it \_a}}+{\it \_C1} \right ) {x}^{2} \right \} \]