2.638   ODE No. 638

\[ y'(x)=y(x) (\log (\log (y(x)))-\log (x)) \] Mathematica : cpu = 0.0941335 (sec), leaf count = 41

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

\[\text {Solve}\left [\int _1^{y(x)}\frac {1}{K[1] (x \log (x)+\log (K[1])-x \log (\log (K[1])))}dK[1]=-\log (x)+c_1,y(x)\right ]\] Maple : cpu = 0.372 (sec), leaf count = 34

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

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