Internal problem ID [8219]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 639.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [y=_G(x,y')]
Solve \begin {gather*} \boxed {y^{\prime }-\left (-\ln \left (\ln \relax (y)\right )+\ln \relax (x )\right )^{2} y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 46
dsolve(diff(y(x),x) = (-ln(ln(y(x)))+ln(x))^2*y(x),y(x), singsol=all)
\[ \int _{\textit {\_b}}^{y \relax (x )}\frac {1}{\textit {\_a} \left (\ln \relax (x )^{2} x -2 \ln \relax (x ) \ln \left (\ln \left (\textit {\_a} \right )\right ) x +\ln \left (\ln \left (\textit {\_a} \right )\right )^{2} x -\ln \left (\textit {\_a} \right )\right )}d \textit {\_a} -c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.121 (sec). Leaf size: 53
DSolve[y'[x] == (Log[x] - Log[Log[y[x]]])^2*y[x],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\int _1^{y(x)}\frac {1}{K[1] \left (x \log ^2(x)-2 x \log (\log (K[1])) \log (x)+x \log ^2(\log (K[1]))-\log (K[1])\right )}dK[1]=\log (x)+c_1,y(x)\right ] \]