\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac { \left ( y \left ( x \right ) \right ) ^{2}}{{x}^{3}} \left ( 2+F \left ( {\frac {{x}^{2}-y \left ( x \right ) }{{x}^{2}y \left ( x \right ) }} \right ) {x}^{2} \right ) }=0} \]
Mathematica: cpu = 46.096854 (sec), leaf count = 164 \[ \text {Solve}\left [\int _1^{y(x)} \left (-\int _1^x -\frac {2 \left (-\frac {K[1]^2-K[2]}{K[1]^2 K[2]^2}-\frac {1}{K[1]^2 K[2]}\right ) F'\left (\frac {K[1]^2-K[2]}{K[1]^2 K[2]}\right )}{K[1]^3 F\left (\frac {K[1]^2-K[2]}{K[1]^2 K[2]}\right )^2} \, dK[1]-\frac {1}{K[2]^2 F\left (\frac {x^2-K[2]}{x^2 K[2]}\right )}\right ) \, dK[2]+\int _1^x \left (\frac {2}{K[1]^3 F\left (\frac {K[1]^2-y(x)}{y(x) K[1]^2}\right )}+\frac {1}{K[1]}\right ) \, dK[1]=c_1,y(x)\right ] \]
Maple: cpu = 0.125 (sec), leaf count = 33 \[ \left \{ y \left ( x \right ) ={\frac {{x}^{2}}{{\it RootOf} \left ( - \ln \left ( x \right ) -\int ^{{\it \_Z}}\! \left ( F \left ( {\it \_a} \right ) \right ) ^{-1}{d{\it \_a}}+{\it \_C1} \right ) {x}^{2}+1}} \right \} \]