50.2.9 problem 1(i)

Internal problem ID [7815]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.3 SEPARABLE EQUATIONS. Page 12
Problem number : 1(i)
Date solved : Monday, January 27, 2025 at 03:23:56 PM
CAS classification : [_separable]

\begin{align*} x y y^{\prime }&=y-1 \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 12

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

\[ y = \operatorname {LambertW}\left (x c_{1} {\mathrm e}^{-1}\right )+1 \]

✓ Solution by Mathematica

Time used: 3.048 (sec). Leaf size: 21

DSolve[x*y[x]*D[y[x],x]==y[x]-1,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to 1+W\left (e^{-1+c_1} x\right ) \\ y(x)\to 1 \\ \end{align*}