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: 640.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [`y=_G(x,y')`]
\[ \boxed {y^{\prime }-\frac {y}{\ln \left (\ln \left (y\right )\right )-\ln \left (x \right )+1}=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 45
dsolve(diff(y(x),x) = 1/(ln(ln(y(x)))-ln(x)+1)*y(x),y(x), singsol=all)
\[ \int _{\textit {\_b}}^{y \left (x \right )}\frac {\ln \left (x \right )-\ln \left (\ln \left (\textit {\_a} \right )\right )-1}{\textit {\_a} \left (-\ln \left (\textit {\_a} \right ) \ln \left (\ln \left (\textit {\_a} \right )\right )+\left (-1+\ln \left (x \right )\right ) \ln \left (\textit {\_a} \right )+x \right )}d \textit {\_a} -c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.238 (sec). Leaf size: 53
DSolve[y'[x] == y[x]/(1 - Log[x] + Log[Log[y[x]]]),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\int _1^{y(x)}\frac {\log (x)-\log (\log (K[1]))-1}{K[1] (x+\log (x) \log (K[1])-\log (K[1])-\log (K[1]) \log (\log (K[1])))}dK[1]=c_1,y(x)\right ] \]