60.1.118 problem 119

Internal problem ID [10132]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 119
Date solved : Monday, January 27, 2025 at 06:29:17 PM
CAS classification : [[_homogeneous, `class G`]]

\begin{align*} x y^{\prime }-y \left (\ln \left (y x \right )-1\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.035 (sec). Leaf size: 14

dsolve(x*diff(y(x),x) - y(x)*(ln(x*y(x))-1)=0,y(x), singsol=all)
 

\[ y = \frac {{\mathrm e}^{\frac {x}{c_{1}}}}{x} \]

✓ Solution by Mathematica

Time used: 0.252 (sec). Leaf size: 26

DSolve[x*D[y[x],x] - y[x]*(Log[x*y[x]]-1)==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {e^{e^{e c_1} x}}{x} \\ y(x)\to \frac {1}{x} \\ \end{align*}