Internal problem ID [8973]
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')`]
\[ \boxed {y^{\prime }+\left (-\ln \left (\ln \left (y\right )\right )+\ln \left (x \right )\right ) y=0} \]
✓ Solution by Maple
Time used: 0.11 (sec). Leaf size: 36
dsolve(diff(y(x),x) = -(-ln(ln(y(x)))+ln(x))*y(x),y(x), singsol=all)
\[ -\left (\int _{\textit {\_b}}^{y \left (x \right )}-\frac {1}{\textit {\_a} \left (x \ln \left (x \right )-\ln \left (\ln \left (\textit {\_a} \right )\right ) x +\ln \left (\textit {\_a} \right )\right )}d \textit {\_a} \right )-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.109 (sec). Leaf size: 41
DSolve[y'[x] == (-Log[x] + Log[Log[y[x]]])*y[x],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\int _1^{y(x)}\frac {1}{K[1] (x \log (x)+\log (K[1])-x \log (\log (K[1])))}dK[1]=-\log (x)+c_1,y(x)\right ] \]