20.4.40 problem Problem 58

Internal problem ID [3675]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.8, Change of Variables. page 79
Problem number : Problem 58
Date solved : Monday, January 27, 2025 at 07:54:27 AM
CAS classification : [[_homogeneous, `class G`]]

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

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 14

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

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

✓ Solution by Mathematica

Time used: 0.218 (sec). Leaf size: 24

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

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