\[ y'(x)=\frac {y(x)^2 F\left (\frac {1-2 y(x) \log (x)}{y(x)}\right )}{x} \] ✓ Mathematica : cpu = 28.1145 (sec), leaf count = 135
\[\text {Solve}\left [c_1=\int _1^{y(x)} -\frac {K[2]^2 \left (F\left (\frac {1}{K[2]}-2 \log (x)\right )+2\right ) \left (\int _1^x -\frac {4 F'\left (\frac {1}{K[2]}-2 \log (K[1])\right )}{K[1] K[2]^2 \left (F\left (\frac {1}{K[2]}-2 \log (K[1])\right )+2\right )^2} \, dK[1]\right )+2}{K[2]^2 \left (F\left (\frac {1}{K[2]}-2 \log (x)\right )+2\right )} \, dK[2]+\int _1^x \frac {2 F\left (\frac {1}{y(x)}-2 \log (K[1])\right )}{K[1] \left (F\left (\frac {1}{y(x)}-2 \log (K[1])\right )+2\right )} \, dK[1],y(x)\right ]\]
✓ Maple : cpu = 6.479 (sec), leaf count = 38
\[ \left \{ \int _{{\it \_b}}^{y \left ( x \right ) }\!{\frac {1}{{{\it \_a}}^{2}} \left ( F \left ( {\frac {-2\,{\it \_a}\,\ln \left ( x \right ) +1}{{\it \_a}}} \right ) +2 \right ) ^{-1}}\,{\rm d}{\it \_a}-\ln \left ( x \right ) -{\it \_C1}=0 \right \} \]