\[ y'(x)=-\frac {y(x)^2 \left (2 x-F\left (\frac {1-\frac {1}{2} x y(x)}{y(x)}\right )\right )}{4 x} \] ✓ Mathematica : cpu = 215.819 (sec), leaf count = 103
\[\text {Solve}\left [c_1=\int _1^{y(x)} \left (-\int _1^x -\frac {2 F'\left (\frac {1}{K[2]}-\frac {K[1]}{2}\right )}{K[2]^2 F\left (\frac {1}{K[2]}-\frac {K[1]}{2}\right )^2} \, dK[1]-\frac {4}{K[2]^2 F\left (\frac {1}{K[2]}-\frac {x}{2}\right )}\right ) \, dK[2]+\int _1^x \left (\frac {1}{K[1]}-\frac {2}{F\left (\frac {1}{y(x)}-\frac {K[1]}{2}\right )}\right ) \, dK[1],y(x)\right ]\]
✓ Maple : cpu = 0.148 (sec), leaf count = 29
\[ \left \{ y \left ( x \right ) =2\, \left ( 2\,{\it RootOf} \left ( -\ln \left ( x \right ) -4\,\int ^{{\it \_Z}}\! \left ( F \left ( {\it \_a} \right ) \right ) ^{-1}{d{\it \_a}}+{\it \_C1} \right ) +x \right ) ^{-1} \right \} \]