Internal problem ID [6208]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven
Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 1. What is a differential equation. Section 1.7. Homogeneous Equations. Page
28
Problem number: 1(f).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {-y-y^{\prime } \left (x +y\right )=-x} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 51
dsolve((x-y(x))-(x+y(x))*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \frac {-c_{1} x -\sqrt {2 c_{1}^{2} x^{2}+1}}{c_{1}} y \left (x \right ) = \frac {-c_{1} x +\sqrt {2 c_{1}^{2} x^{2}+1}}{c_{1}} \end{align*}
✓ Solution by Mathematica
Time used: 0.493 (sec). Leaf size: 94
DSolve[(x-y[x])-(x+y[x])*y'[x]==0,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*}