\[ y'(x)=\frac {y(x)^2 F\left (\frac {1-y(x) \log (x)}{y(x)}\right )}{x} \] ✓ Mathematica : cpu = 25.5005 (sec), leaf count = 242
\[\text {Solve}\left [\int _1^{y(x)} \left (\frac {1}{K[2]^2 \left (-F\left (\frac {1-\log (x) K[2]}{K[2]}\right )-1\right )}-\int _1^x \left (\frac {\left (-\frac {\log (K[1])}{K[2]}-\frac {1-K[2] \log (K[1])}{K[2]^2}\right ) F'\left (\frac {1-K[2] \log (K[1])}{K[2]}\right )}{K[1] \left (F\left (\frac {1-K[2] \log (K[1])}{K[2]}\right )+1\right )}-\frac {\left (-\frac {\log (K[1])}{K[2]}-\frac {1-K[2] \log (K[1])}{K[2]^2}\right ) F\left (\frac {1-K[2] \log (K[1])}{K[2]}\right ) F'\left (\frac {1-K[2] \log (K[1])}{K[2]}\right )}{K[1] \left (F\left (\frac {1-K[2] \log (K[1])}{K[2]}\right )+1\right )^2}\right ) \, dK[1]\right ) \, dK[2]+\int _1^x \frac {F\left (\frac {1-y(x) \log (K[1])}{y(x)}\right )}{K[1] \left (F\left (\frac {1-y(x) \log (K[1])}{y(x)}\right )+1\right )} \, dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.159 (sec), leaf count = 38
\[ \left \{ \int _{{\it \_b}}^{y \left ( x \right ) }\!{\frac {1}{{{\it \_a}}^{2}} \left ( F \left ( {\frac {1-{\it \_a}\,\ln \left ( x \right ) }{{\it \_a}}} \right ) +1 \right ) ^{-1}}\,{\rm d}{\it \_a}-\ln \left ( x \right ) -{\it \_C1}=0 \right \} \]