2.639   ODE No. 639

\[ y'(x)=y(x) (\log (x)-\log (\log (y(x))))^2 \]

✓ Mathematica : cpu = 0.131032 (sec), leaf count = 53

DSolve[Derivative[1][y][x] == (Log[x] - Log[Log[y[x]]])^2*y[x],y[x],x]
 

\[\text {Solve}\left [\int _1^{y(x)}\frac {1}{K[1] \left (x \log ^2(x)-2 x \log (\log (K[1])) \log (x)+x \log ^2(\log (K[1]))-\log (K[1])\right )}dK[1]=\log (x)+c_1,y(x)\right ]\]

✓ Maple : cpu = 0.395 (sec), leaf count = 46

dsolve(diff(y(x),x) = (-ln(ln(y(x)))+ln(x))^2*y(x),y(x))
 

\[\int _{\textit {\_b}}^{y \left (x \right )}\frac {1}{\textit {\_a} \left (x \ln \left (x \right )^{2}-2 \ln \left (\ln \left (\textit {\_a} \right )\right ) \ln \left (x \right ) x +\ln \left (\ln \left (\textit {\_a} \right )\right )^{2} x -\ln \left (\textit {\_a} \right )\right )}d \textit {\_a} -c_{1} = 0\]