78.8.47 problem 47

Internal problem ID [18245]
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. Miscellaneous Problems for Chapter 2. Problems at page 99
Problem number : 47
Date solved : Tuesday, January 28, 2025 at 11:44:08 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 16

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

\[ y = \frac {{\mathrm e}^{-x} c_{1} +1}{x} \]

✓ Solution by Mathematica

Time used: 0.035 (sec). Leaf size: 19

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

\[ y(x)\to \frac {1+c_1 e^{-x}}{x} \]