\[ y'(x)=\frac {x F\left (\frac {x^2 y(x)+\frac {1}{4}}{x^2}\right )+\frac {1}{2}}{x^3} \] ✓ Mathematica : cpu = 0.233556 (sec), leaf count = 144
\[\text {Solve}\left [\int _1^{y(x)}-\frac {F\left (\frac {K[2] x^2+\frac {1}{4}}{x^2}\right ) \int _1^x-\frac {F'\left (\frac {K[2] K[1]^2+\frac {1}{4}}{K[1]^2}\right )}{2 F\left (\frac {K[2] K[1]^2+\frac {1}{4}}{K[1]^2}\right )^2 K[1]^3}dK[1]+1}{F\left (\frac {K[2] x^2+\frac {1}{4}}{x^2}\right )}dK[2]+\int _1^x\left (\frac {1}{K[1]^2}+\frac {1}{2 K[1]^3 F\left (\frac {y(x) K[1]^2+\frac {1}{4}}{K[1]^2}\right )}\right )dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.216 (sec), leaf count = 32
\[ \left \{ y \left ( x \right ) ={\frac {4\,{\it RootOf} \left ( \int ^{{\it \_Z}}\! \left ( F \left ( {\it \_a} \right ) \right ) ^{-1}{d{\it \_a}}x+{\it \_C1}\,x+1 \right ) {x}^{2}-1}{4\,{x}^{2}}} \right \} \]