Internal problem ID [96]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {\left (x +y\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 11
dsolve((x+y(x))*diff(y(x),x) = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = -x y \left (x \right ) = c_{1} \end{align*}
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 14
DSolve[(x+y[x])*y'[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x y(x)\to c_1 \end{align*}