8.5.18 problem 18

Internal problem ID [746]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.6, Substitution methods and exact equations. Page 74
Problem number : 18
Date solved : Monday, January 27, 2025 at 03:02:22 AM
CAS classification : [_quadrature]

\begin{align*} \left (x +y\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 11

dsolve((x+y(x))*diff(y(x),x) = 0,y(x), singsol=all)
 

\begin{align*} y &= -x \\ y &= c_1 \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 14

DSolve[(x+y[x])*D[y[x],x] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -x \\ y(x)\to c_1 \\ \end{align*}