\[ y'(x)=\frac {x F\left (\frac {x^2 y(x)+\frac {1}{4}}{x^2}\right )+\frac {1}{2}}{x^3} \] ✓ Mathematica : cpu = 48.2061 (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 = 0.103 (sec), leaf count = 32
\[ \left \{ y \left ( x \right ) ={\frac {4\,{\it RootOf} \left ( \int ^{{\it \_Z}}\! \left ( F \left ( {\it \_a} \right ) \right ) ^{-1}{d{\it \_a}}x+x{\it \_C1}+1 \right ) {x}^{2}-1}{4\,{x}^{2}}} \right \} \]