7.5.1 problem 1

Internal problem ID [105]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.6 (substitution and exact equations). Problems at page 72
Problem number : 1
Date solved : Friday, February 07, 2025 at 07:49:34 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: 0.044 (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: 0.527 (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*}