\[ y'(x)=-\frac {y(x)^2 \left (2 x-F\left (\frac {1-\frac {1}{2} x y(x)}{y(x)}\right )\right )}{4 x} \] ✓ Mathematica : cpu = 0.450136 (sec), leaf count = 145
\[\text {Solve}\left [\int _1^{y(x)}\left (-\int _1^x\frac {2 \left (-\frac {K[1]}{2 K[2]}-\frac {1-\frac {1}{2} K[1] K[2]}{K[2]^2}\right ) F'\left (\frac {1-\frac {1}{2} K[1] K[2]}{K[2]}\right )}{F\left (\frac {1-\frac {1}{2} K[1] K[2]}{K[2]}\right )^2}dK[1]-\frac {4}{F\left (\frac {1-\frac {1}{2} x K[2]}{K[2]}\right ) K[2]^2}\right )dK[2]+\int _1^x\left (\frac {1}{K[1]}-\frac {2}{F\left (\frac {1-\frac {1}{2} K[1] y(x)}{y(x)}\right )}\right )dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.295 (sec), leaf count = 29
\[ \left \{ y \left ( x \right ) =2\, \left ( 2\,{\it RootOf} \left ( -\ln \left ( x \right ) -4\,\int ^{{\it \_Z}}\! \left ( F \left ( {\it \_a} \right ) \right ) ^{-1}{d{\it \_a}}+{\it \_C1} \right ) +x \right ) ^{-1} \right \} \]