8.5.1 problem 1

Internal problem ID [729]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.6, Substitution methods and exact equations. Page 74
Problem number : 1
Date solved : Monday, January 27, 2025 at 02:59:22 AM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.024 (sec). Leaf size: 51

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

\begin{align*} y &= \frac {-c_1 x -\sqrt {2 c_1^{2} x^{2}+1}}{c_1} \\ y &= \frac {-c_1 x +\sqrt {2 c_1^{2} x^{2}+1}}{c_1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.414 (sec). Leaf size: 94

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

\begin{align*} y(x)\to -x-\sqrt {2 x^2+e^{2 c_1}} \\ y(x)\to -x+\sqrt {2 x^2+e^{2 c_1}} \\ y(x)\to -\sqrt {2} \sqrt {x^2}-x \\ y(x)\to \sqrt {2} \sqrt {x^2}-x \\ \end{align*}