Internal problem ID [6147]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {x y y^{\prime }-y=-1} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 12
dsolve(x*y(x)*diff(y(x),x)=y(x)-1,y(x), singsol=all)
\[ y \left (x \right ) = \operatorname {LambertW}\left (x c_{1} {\mathrm e}^{-1}\right )+1 \]
✓ Solution by Mathematica
Time used: 3.215 (sec). Leaf size: 21
DSolve[x*y[x]*y'[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*}