2.640   ODE No. 640

\[ y'(x)=\frac {y(x)}{\log (\log (y(x)))-\log (x)+1} \]

✓ Mathematica : cpu = 0.198646 (sec), leaf count = 53

DSolve[Derivative[1][y][x] == y[x]/(1 - Log[x] + Log[Log[y[x]]]),y[x],x]
 

\[\text {Solve}\left [\int _1^{y(x)}\frac {\log (x)-\log (\log (K[1]))-1}{K[1] (x+\log (x) \log (K[1])-\log (K[1])-\log (K[1]) \log (\log (K[1])))}dK[1]=c_1,y(x)\right ]\]

✓ Maple : cpu = 0.744 (sec), leaf count = 47

dsolve(diff(y(x),x) = 1/(ln(ln(y(x)))-ln(x)+1)*y(x),y(x))
 

\[\int _{\textit {\_b}}^{y \left (x \right )}\frac {-\ln \left (\ln \left (\textit {\_a} \right )\right )+\ln \left (x \right )-1}{\left (-\ln \left (\textit {\_a} \right ) \ln \left (\ln \left (\textit {\_a} \right )\right )+\ln \left (\textit {\_a} \right ) \ln \left (x \right )-\ln \left (\textit {\_a} \right )+x \right ) \textit {\_a}}d \textit {\_a} -c_{1} = 0\]