\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =1/2\,{\frac {1}{{x}^{3}} \left ( 1+2\,F \left ( 1/4\,{\frac {4\,{x}^{2}y \left ( x \right ) +1}{{x}^{2}}} \right ) x \right ) }=0} \]
Mathematica: cpu = 40.986705 (sec), leaf count = 141 \[ \text {Solve}\left [\int _1^{y(x)} -\frac {F\left (\frac {x^2 K[2]+\frac {1}{4}}{x^2}\right ) \int _1^x -\frac {F'\left (\frac {K[2] K[1]^2+\frac {1}{4}}{K[1]^2}\right )}{2 K[1]^3 F\left (\frac {K[2] K[1]^2+\frac {1}{4}}{K[1]^2}\right )^2} \, dK[1]+1}{F\left (\frac {x^2 K[2]+\frac {1}{4}}{x^2}\right )} \, dK[2]+\int _1^x \left (\frac {1}{2 K[1]^3 F\left (\frac {y(x) K[1]^2+\frac {1}{4}}{K[1]^2}\right )}+\frac {1}{K[1]^2}\right ) \, dK[1]=c_1,y(x)\right ] \]
Maple: cpu = 0.093 (sec), leaf count = 32 \[ \left \{ y \left ( x \right ) ={\frac {4\,{\it RootOf} \left ( \int ^{{ \it \_Z}}\! \left ( F \left ( {\it \_a} \right ) \right ) ^{-1}{d{\it \_a }}x+{\it \_C1}\,x+1 \right ) {x}^{2}-1}{4\,{x}^{2}}} \right \} \]