60.2.64 problem 640

Internal problem ID [10651]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 640
Date solved : Tuesday, January 28, 2025 at 05:01:54 PM
CAS classification : [`y=_G(x,y')`]

\begin{align*} y^{\prime }&=\frac {y}{\ln \left (\ln \left (y\right )\right )-\ln \left (x \right )+1} \end{align*}

✓ Solution by Maple

Time used: 1.074 (sec). Leaf size: 45

dsolve(diff(y(x),x) = 1/(ln(ln(y(x)))-ln(x)+1)*y(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.193 (sec). Leaf size: 53

DSolve[D[y[x],x] == y[x]/(1 - Log[x] + Log[Log[y[x]]]),y[x],x,IncludeSingularSolutions -> True]
 

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