\[ y'(x)=\frac {x F\left (\frac {x^2 y(x)+\frac {1}{4}}{x^2}\right )+\frac {1}{2}}{x^3} \] ✓ Mathematica : cpu = 48.465 (sec), leaf count = 107
\[\text {Solve}\left [c_1=\int _1^{y(x)} \left (-\int _1^x -\frac {F'\left (K[2]+\frac {1}{4 K[1]^2}\right )}{2 K[1]^3 F\left (K[2]+\frac {1}{4 K[1]^2}\right )^2} \, dK[1]-\frac {1}{F\left (K[2]+\frac {1}{4 x^2}\right )}\right ) \, dK[2]+\int _1^x \frac {\frac {1}{F\left (\frac {1}{4 K[1]^2}+y(x)\right )}+2 K[1]}{2 K[1]^3} \, dK[1],y(x)\right ]\]
✓ Maple : cpu = 0.37 (sec), leaf count = 32
\[ \left \{ y \left ( x \right ) ={\frac {4\,{\it RootOf} \left ( \int ^{{\it \_Z}}\! \left ( F \left ( {\it \_a} \right ) \right ) ^{-1}{d{\it \_a}}x+{\it \_C1}\,x+1 \right ) {x}^{2}-1}{4\,{x}^{2}}} \right \} \]