\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =F \left ( \ln \left ( \ln \left ( y \left ( x \right ) \right ) \right ) -\ln \left ( x \right ) \right ) y \left ( x \right ) =0} \]
Mathematica: cpu = 123.303658 (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 = 0.406 (sec), leaf count = 163 \[ \left \{ \int _{{\it \_b}}^{x}\!{\frac {F \left ( \ln \left ( \ln \left ( y \left ( x \right ) \right ) \right ) -\ln \left ( {\it \_a} \right ) \right ) }{-{\it \_a}\,F \left ( \ln \left ( \ln \left ( y \left ( x \right ) \right ) \right ) -\ln \left ( {\it \_a} \right ) \right ) +\ln \left ( y \left ( x \right ) \right ) }}\,{\rm d}{\it \_a} +\int ^{y \left ( x \right ) }\!-{\frac {1}{{\it \_f}\, \left ( -xF \left ( \ln \left ( \ln \left ( {\it \_f} \right ) \right ) -\ln \left ( x \right ) \right ) +\ln \left ( {\it \_f} \right ) \right ) }}- \int _{{\it \_b}}^{x}\!{\frac {\mbox {D} \left ( F \right ) \left ( \ln \left ( \ln \left ( {\it \_f} \right ) \right ) -\ln \left ( {\it \_a} \right ) \right ) }{{\it \_f}\,\ln \left ( {\it \_f} \right ) \left ( - {\it \_a}\,F \left ( \ln \left ( \ln \left ( {\it \_f} \right ) \right ) -\ln \left ( {\it \_a} \right ) \right ) +\ln \left ( {\it \_f } \right ) \right ) }}-{\frac {F \left ( \ln \left ( \ln \left ( {\it \_f} \right ) \right ) -\ln \left ( {\it \_a} \right ) \right ) }{ \left ( -{\it \_a}\,F \left ( \ln \left ( \ln \left ( {\it \_f} \right ) \right ) -\ln \left ( {\it \_a} \right ) \right ) +\ln \left ( {\it \_f} \right ) \right ) ^{2}} \left ( -{\frac {{\it \_a}\, \mbox {D} \left ( F \right ) \left ( \ln \left ( \ln \left ( {\it \_f} \right ) \right ) -\ln \left ( {\it \_a} \right ) \right ) }{{\it \_f} \,\ln \left ( {\it \_f} \right ) }}+{{\it \_f}}^{-1} \right ) }\,{\rm d} {\it \_a}{d{\it \_f}}+{\it \_C1}=0 \right \} \]