60.1.93 problem 93

Internal problem ID [10107]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 93
Date solved : Monday, January 27, 2025 at 06:27:45 PM
CAS classification : [_linear]

\begin{align*} x y^{\prime }-y-\frac {x \cos \left (\ln \left (\ln \left (x \right )\right )\right )}{\ln \left (x \right )}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 12

dsolve(x*diff(y(x),x) - y(x) - x*cos(ln(ln(x)))/ln(x)=0,y(x), singsol=all)
 

\[ y = \left (\sin \left (\ln \left (\ln \left (x \right )\right )\right )+c_{1} \right ) x \]

✓ Solution by Mathematica

Time used: 0.092 (sec). Leaf size: 32

DSolve[x*D[y[x],x] - y[x] - x*Cos[Log[Log[x]]]/Log[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x \left (\int _1^x\frac {\cos (\log (\log (K[1])))}{K[1] \log (K[1])}dK[1]+c_1\right ) \]