\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac { \left ( y \left ( x \right ) \right ) ^{2}}{x}F \left ( -{\frac {2\,y \left ( x \right ) \ln \left ( x \right ) -1}{y \left ( x \right ) }} \right ) }=0} \]
Mathematica: cpu = 24.086559 (sec), leaf count = 243 \[ \text {Solve}\left [\int _1^{y(x)} \left (-\int _1^x \left (\frac {2 \left (-\frac {2 \log (K[1])}{K[2]}-\frac {1-2 K[2] \log (K[1])}{K[2]^2}\right ) F'\left (\frac {1-2 K[2] \log (K[1])}{K[2]}\right )}{K[1] \left (F\left (\frac {1-2 K[2] \log (K[1])}{K[2]}\right )+2\right )}-\frac {2 \left (-\frac {2 \log (K[1])}{K[2]}-\frac {1-2 K[2] \log (K[1])}{K[2]^2}\right ) F\left (\frac {1-2 K[2] \log (K[1])}{K[2]}\right ) F'\left (\frac {1-2 K[2] \log (K[1])}{K[2]}\right )}{K[1] \left (F\left (\frac {1-2 K[2] \log (K[1])}{K[2]}\right )+2\right )^2}\right ) \, dK[1]-\frac {2}{K[2]^2 \left (F\left (\frac {1-2 \log (x) K[2]}{K[2]}\right )+2\right )}\right ) \, dK[2]+\int _1^x \frac {2 F\left (\frac {1-2 y(x) \log (K[1])}{y(x)}\right )}{K[1] \left (F\left (\frac {1-2 y(x) \log (K[1])}{y(x)}\right )+2\right )} \, dK[1]=c_1,y(x)\right ] \]
Maple: cpu = 0.141 (sec), leaf count = 38 \[ \left \{ \int _{{\it \_b}}^{y \left ( x \right ) }\!{\frac {1}{{{\it \_a} }^{2}} \left ( F \left ( {\frac {-2\,{\it \_a}\,\ln \left ( x \right ) +1 }{{\it \_a}}} \right ) +2 \right ) ^{-1}}\,{\rm d}{\it \_a}-\ln \left ( x \right ) -{\it \_C1}=0 \right \} \]