73.5.18 problem 6.7 (f)

Internal problem ID [15129]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 6. Simplifying through simplifiction. Additional exercises. page 114
Problem number : 6.7 (f)
Date solved : Tuesday, January 28, 2025 at 07:34:59 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (x +y\right ) y^{\prime }&=y \end{align*}

✓ Solution by Maple

Time used: 0.043 (sec). Leaf size: 13

dsolve((y(x)+x)*diff(y(x),x)=y(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 3.727 (sec). Leaf size: 25

DSolve[(y[x]+x)*D[y[x],x]==y[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {x}{W\left (e^{-1-c_1} x\right )} \\ y(x)\to 0 \\ \end{align*}