64.5.9 problem 9

Internal problem ID [13322]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, section 2.3 (Linear equations). Exercises page 56
Problem number : 9
Date solved : Tuesday, January 28, 2025 at 05:22:09 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 16

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

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

✓ Solution by Mathematica

Time used: 0.054 (sec). Leaf size: 21

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

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