\[ y'(x)=y(x) F(\log (\log (y(x)))-\log (x)) \] ✓ Mathematica : cpu = 0.274639 (sec), leaf count = 205
\[\text {Solve}\left [\int _1^{y(x)}\left (\frac {1}{K[2] (x F(\log (\log (K[2]))-\log (x))-\log (K[2]))}-\int _1^x\left (\frac {F(\log (\log (K[2]))-\log (K[1])) \left (\frac {K[1] F'(\log (\log (K[2]))-\log (K[1]))}{K[2] \log (K[2])}-\frac {1}{K[2]}\right )}{(F(\log (\log (K[2]))-\log (K[1])) K[1]-\log (K[2]))^2}-\frac {F'(\log (\log (K[2]))-\log (K[1]))}{K[2] (F(\log (\log (K[2]))-\log (K[1])) K[1]-\log (K[2])) \log (K[2])}\right )dK[1]\right )dK[2]+\int _1^x-\frac {F(\log (\log (y(x)))-\log (K[1]))}{F(\log (\log (y(x)))-\log (K[1])) K[1]-\log (y(x))}dK[1]=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.451 (sec), leaf count = 120
\[\left \{c_{1}+\int _{\textit {\_b}}^{x}\frac {F \left (-\ln \left (\textit {\_a} \right )+\ln \left (\ln \left (y \left (x \right )\right )\right )\right )}{\textit {\_a} F \left (-\ln \left (\textit {\_a} \right )+\ln \left (\ln \left (y \left (x \right )\right )\right )\right )-\ln \left (y \left (x \right )\right )}d \textit {\_a} +\int _{}^{y \left (x \right )}\left (-\left (\int _{\textit {\_b}}^{x}\frac {F \left (-\ln \left (\textit {\_a} \right )+\ln \left (\ln \left (\textit {\_f} \right )\right )\right )-D\left (F \right )\left (-\ln \left (\textit {\_a} \right )+\ln \left (\ln \left (\textit {\_f} \right )\right )\right )}{\left (\textit {\_a} F \left (-\ln \left (\textit {\_a} \right )+\ln \left (\ln \left (\textit {\_f} \right )\right )\right )-\ln \left (\textit {\_f} \right )\right )^{2} \textit {\_f}}d \textit {\_a} \right )+\frac {1}{\left (-x F \left (-\ln \left (x \right )+\ln \left (\ln \left (\textit {\_f} \right )\right )\right )+\ln \left (\textit {\_f} \right )\right ) \textit {\_f}}\right )d \textit {\_f} = 0\right \}\]