\[ y'(x)=\frac {y(x)^2 F\left (\frac {1-y(x) \log (x)}{y(x)}\right )}{x} \] ✓ Mathematica : cpu = 25.5939 (sec), leaf count = 118
\[\text {Solve}\left [c_1=\int _1^{y(x)} \left (-\int _1^x -\frac {F'\left (\frac {1}{K[2]}-\log (K[1])\right )}{K[1] K[2]^2 \left (F\left (\frac {1}{K[2]}-\log (K[1])\right )+1\right )^2} \, dK[1]-\frac {1}{K[2]^2 \left (F\left (\frac {1}{K[2]}-\log (x)\right )+1\right )}\right ) \, dK[2]+\int _1^x \frac {F\left (\frac {1}{y(x)}-\log (K[1])\right )}{K[1] \left (F\left (\frac {1}{y(x)}-\log (K[1])\right )+1\right )} \, dK[1],y(x)\right ]\]
✓ Maple : cpu = 0.168 (sec), leaf count = 38
\[ \left \{ \int _{{\it \_b}}^{y \left ( x \right ) }\!{\frac {1}{{{\it \_a}}^{2}} \left ( F \left ( {\frac {1-{\it \_a}\,\ln \left ( x \right ) }{{\it \_a}}} \right ) +1 \right ) ^{-1}}\,{\rm d}{\it \_a}-\ln \left ( x \right ) -{\it \_C1}=0 \right \} \]