68.5.9 problem 9

Internal problem ID [17260]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.3, page 49
Problem number : 9
Date solved : Thursday, October 02, 2025 at 02:00:07 PM
CAS classification : [_linear]

\begin{align*} x y^{\prime }+y&={\mathrm e}^{-x} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 16

ode:=x*diff(y(x),x)+y(x) = exp(-x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {-{\mathrm e}^{-x}+c_1}{x} \]

✓ Mathematica. Time used: 0.033 (sec). Leaf size: 20

ode=x*D[y[x],x]+y[x]==Exp[-x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {e^{-x}-c_1}{x} \end{align*}

✓ Sympy. Time used: 0.143 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*Derivative(y(x), x) + y(x) - exp(-x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} - e^{- x}}{x} \]