2.62 problem 638

Internal problem ID [8218]

Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 638.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [x=_G(y,y')]

Solve \begin {gather*} \boxed {y^{\prime }+\left (-\ln \left (\ln \relax (y)\right )+\ln \relax (x )\right ) y=0} \end {gather*}

Solution by Maple

Time used: 0.395 (sec). Leaf size: 33

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

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

Solution by Mathematica

Time used: 0.102 (sec). Leaf size: 41

DSolve[y'[x] == (-Log[x] + Log[Log[y[x]]])*y[x],y[x],x,IncludeSingularSolutions -> True]
 

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