60.2.62 problem 638

Internal problem ID [10649]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 638
Date solved : Tuesday, January 28, 2025 at 05:01:47 PM
CAS classification : [`x=_G(y,y')`]

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

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 36

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

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

✓ Solution by Mathematica

Time used: 0.091 (sec). Leaf size: 41

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

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