32.6.25 problem Exercise 12.25, page 103

Internal problem ID [5890]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 12, Miscellaneous Methods
Problem number : Exercise 12.25, page 103
Date solved : Monday, January 27, 2025 at 01:24:53 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: 0.025 (sec). Leaf size: 14

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

\[ y \left (x \right ) = \frac {{\mathrm e}^{\frac {x}{c_{1}}}}{x} \]

✓ Solution by Mathematica

Time used: 0.298 (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*}