78.5.17 problem 4 (f)

Internal problem ID [18160]
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 9 (Integrating Factors). Problems at page 80
Problem number : 4 (f)
Date solved : Tuesday, January 28, 2025 at 11:34:34 AM
CAS classification : [_separable]

\begin{align*} y^{2}-y+x y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 11

dsolve((y(x)^2-y(x))+x*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = \frac {x}{x +c_1} \]

✓ Solution by Mathematica

Time used: 0.256 (sec). Leaf size: 25

DSolve[(y[x]^2-y[x])+x*D[y[x],x] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {x}{x+e^{c_1}} \\ y(x)\to 0 \\ y(x)\to 1 \\ \end{align*}