78.3.6 problem 1 (f)

Internal problem ID [18109]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Section 7 (Homogeneous Equations). Problems at page 67
Problem number : 1 (f)
Date solved : Tuesday, January 28, 2025 at 11:28:14 AM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.020 (sec). Leaf size: 51

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

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

✓ Solution by Mathematica

Time used: 0.445 (sec). Leaf size: 94

DSolve[(x-y[x])-(x+y[x])*D[y[x],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*}