\[ y'(x)=\frac {y(x)^2 F\left (\frac {1-y(x) \log (x)}{y(x)}\right )}{x} \] ✓ Mathematica : cpu = 0.228083 (sec), leaf count = 245
\[\text {Solve}\left [\int _1^{y(x)}\left (\frac {1}{\left (-F\left (\frac {1-K[2] \log (x)}{K[2]}\right )-1\right ) K[2]^2}-\int _1^x\left (\frac {\left (-\frac {\log (K[1])}{K[2]}-\frac {1-K[2] \log (K[1])}{K[2]^2}\right ) F'\left (\frac {1-K[2] \log (K[1])}{K[2]}\right )}{\left (F\left (\frac {1-K[2] \log (K[1])}{K[2]}\right )+1\right ) K[1]}-\frac {F\left (\frac {1-K[2] \log (K[1])}{K[2]}\right ) \left (-\frac {\log (K[1])}{K[2]}-\frac {1-K[2] \log (K[1])}{K[2]^2}\right ) F'\left (\frac {1-K[2] \log (K[1])}{K[2]}\right )}{\left (F\left (\frac {1-K[2] \log (K[1])}{K[2]}\right )+1\right )^2 K[1]}\right )dK[1]\right )dK[2]+\int _1^x\frac {F\left (\frac {1-\log (K[1]) y(x)}{y(x)}\right )}{\left (F\left (\frac {1-\log (K[1]) y(x)}{y(x)}\right )+1\right ) K[1]}dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.107 (sec), leaf count = 38
\[ \left \{ \int _{{\it \_b}}^{y \left ( x \right ) }\!{\frac {1}{{{\it \_a}}^{2}} \left ( F \left ( {\frac {1-{\it \_a}\,\ln \left ( x \right ) }{{\it \_a}}} \right ) +1 \right ) ^{-1}}\,{\rm d}{\it \_a}-\ln \left ( x \right ) -{\it \_C1}=0 \right \} \]