60.2.63 problem 639

Internal problem ID [10650]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 639
Date solved : Tuesday, January 28, 2025 at 05:01:50 PM
CAS classification : [`y=_G(x,y')`]

\begin{align*} y^{\prime }&=\left (-\ln \left (\ln \left (y\right )\right )+\ln \left (x \right )\right )^{2} y \end{align*}

✓ Solution by Maple

Time used: 0.062 (sec). Leaf size: 48

dsolve(diff(y(x),x) = (-ln(ln(y(x)))+ln(x))^2*y(x),y(x), singsol=all)
 

\[ -\int _{\textit {\_b}}^{y}\frac {1}{\textit {\_a} \left (\ln \left (x \right )^{2} x -2 \ln \left (x \right ) \ln \left (\ln \left (\textit {\_a} \right )\right ) x +\ln \left (\ln \left (\textit {\_a} \right )\right )^{2} x -\ln \left (\textit {\_a} \right )\right )}d \textit {\_a} -c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.121 (sec). Leaf size: 53

DSolve[D[y[x],x] == (Log[x] - Log[Log[y[x]]])^2*y[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^{y(x)}\frac {1}{K[1] \left (x \log ^2(x)-2 x \log (\log (K[1])) \log (x)+x \log ^2(\log (K[1]))-\log (K[1])\right )}dK[1]=\log (x)+c_1,y(x)\right ] \]