Internal problem ID [5394]
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]
Solve \begin {gather*} \boxed {x y y^{\prime }-y+1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.018 (sec). Leaf size: 12
dsolve(x*y(x)*diff(y(x),x)=y(x)-1,y(x), singsol=all)
\[ y \relax (x ) = \LambertW \left (x c_{1} {\mathrm e}^{-1}\right )+1 \]
✓ Solution by Mathematica
Time used: 4.72 (sec). Leaf size: 21
DSolve[x*y[x]*y'[x]==y[x]-1,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 1+\text {ProductLog}\left (e^{-1+c_1} x\right ) \\ y(x)\to 1 \\ \end{align*}