78.1.23 problem 2 (i)

Internal problem ID [18078]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 1. The Nature of Differential Equations. Separable Equations. Section 2. Problems at page 9
Problem number : 2 (i)
Date solved : Tuesday, January 28, 2025 at 11:25:34 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.066 (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: 1.575 (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*}