#### 2.585   ODE No. 585

$y'(x)=y(x) F(\log (\log (y(x)))-\log (x))$ Mathematica : cpu = 0.210344 (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 = 2.681 (sec), leaf count = 120

$\left \{ \int _{{\it \_b}}^{x}\!{\frac {F \left ( \ln \left ( \ln \left ( y \left ( x \right ) \right ) \right ) -\ln \left ( {\it \_a} \right ) \right ) }{{\it \_a}\,F \left ( \ln \left ( \ln \left ( y \left ( x \right ) \right ) \right ) -\ln \left ( {\it \_a} \right ) \right ) -\ln \left ( y \left ( x \right ) \right ) }}\,{\rm d}{\it \_a}+\int ^{y \left ( x \right ) }\!{\frac {1}{{\it \_f}\, \left ( -xF \left ( \ln \left ( \ln \left ( {\it \_f} \right ) \right ) -\ln \left ( x \right ) \right ) +\ln \left ( {\it \_f} \right ) \right ) }}-\int _{{\it \_b}}^{x}\!{\frac {F \left ( \ln \left ( \ln \left ( {\it \_f} \right ) \right ) -\ln \left ( {\it \_a} \right ) \right ) -\mbox {D} \left ( F \right ) \left ( \ln \left ( \ln \left ( {\it \_f} \right ) \right ) -\ln \left ( {\it \_a} \right ) \right ) }{ \left ( {\it \_a}\,F \left ( \ln \left ( \ln \left ( {\it \_f} \right ) \right ) -\ln \left ( {\it \_a} \right ) \right ) -\ln \left ( {\it \_f} \right ) \right ) ^{2}{\it \_f}}}\,{\rm d}{\it \_a}{d{\it \_f}}+{\it \_C1}=0 \right \}$