\[ y'(x)=y(x) F(\log (\log (y(x)))-\log (x)) \] ✓ Mathematica : cpu = 122.928 (sec), leaf count = 202
\[\text {Solve}\left [\int _1^{y(x)} \left (\frac {1}{K[2] (x F(\log (\log (K[2]))-\log (x))-\log (K[2]))}-\int _1^x \left (\frac {F(\log (\log (K[2]))-\log (K[1])) \left (\frac {K[1] F'(\log (\log (K[2]))-\log (K[1]))}{K[2] \log (K[2])}-\frac {1}{K[2]}\right )}{(K[1] F(\log (\log (K[2]))-\log (K[1]))-\log (K[2]))^2}-\frac {F'(\log (\log (K[2]))-\log (K[1]))}{K[2] \log (K[2]) (K[1] F(\log (\log (K[2]))-\log (K[1]))-\log (K[2]))}\right ) \, dK[1]\right ) \, dK[2]+\int _1^x -\frac {F(\log (\log (y(x)))-\log (K[1]))}{K[1] F(\log (\log (y(x)))-\log (K[1]))-\log (y(x))} \, dK[1]=c_1,y(x)\right ]\]
✓ Maple : cpu = 0.47 (sec), leaf count = 168
\[ \left \{ \int _{{\it \_b}}^{x}\!{\frac {F \left ( \ln \left ( \ln \left ( y \left ( x \right ) \right ) \right ) -\ln \left ( {\it \_a} \right ) \right ) }{{\it \_a}\,F \left ( \ln \left ( \ln \left ( y \left ( x \right ) \right ) \right ) -\ln \left ( {\it \_a} \right ) \right ) -\ln \left ( y \left ( x \right ) \right ) }}\,{\rm d}{\it \_a}+\int ^{y \left ( x \right ) }\!-{\frac {1}{{\it \_f}\, \left ( xF \left ( \ln \left ( \ln \left ( {\it \_f} \right ) \right ) -\ln \left ( x \right ) \right ) -\ln \left ( {\it \_f} \right ) \right ) }}-\int _{{\it \_b}}^{x}\!-{\frac {F \left ( \ln \left ( \ln \left ( {\it \_f} \right ) \right ) -\ln \left ( {\it \_a} \right ) \right ) }{ \left ( {\it \_a}\,F \left ( \ln \left ( \ln \left ( {\it \_f} \right ) \right ) -\ln \left ( {\it \_a} \right ) \right ) -\ln \left ( {\it \_f} \right ) \right ) ^{2}} \left ( {\frac {{\it \_a}\,\mbox {D} \left ( F \right ) \left ( \ln \left ( \ln \left ( {\it \_f} \right ) \right ) -\ln \left ( {\it \_a} \right ) \right ) }{{\it \_f}\,\ln \left ( {\it \_f} \right ) }}-{{\it \_f}}^{-1} \right ) }+{\frac {\mbox {D} \left ( F \right ) \left ( \ln \left ( \ln \left ( {\it \_f} \right ) \right ) -\ln \left ( {\it \_a} \right ) \right ) }{ \left ( {\it \_a}\,F \left ( \ln \left ( \ln \left ( {\it \_f} \right ) \right ) -\ln \left ( {\it \_a} \right ) \right ) -\ln \left ( {\it \_f} \right ) \right ) {\it \_f}\,\ln \left ( {\it \_f} \right ) }}\,{\rm d}{\it \_a}{d{\it \_f}}+{\it \_C1}=0 \right \} \]