60.1.91 problem 91

Internal problem ID [10105]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 91
Date solved : Monday, January 27, 2025 at 06:27:41 PM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 11

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

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

✓ Solution by Mathematica

Time used: 0.033 (sec). Leaf size: 13

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

\[ y(x)\to x (\log (\log (x))+c_1) \]