78.4.8 problem 9

Internal problem ID [18131]
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 8 (Exact Equations). Problems at page 72
Problem number : 9
Date solved : Tuesday, January 28, 2025 at 11:30:46 AM
CAS classification : [_separable]

\begin{align*} 1+y+\left (1-x \right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 11

dsolve((1+y(x))+(1-x)*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = -1+\left (x -1\right ) c_1 \]

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 18

DSolve[(1+y[x])+(1-x)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -1+c_1 (x-1) \\ y(x)\to -1 \\ \end{align*}