68.5.25 problem 25

Internal problem ID [17276]
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 : 25
Date solved : Thursday, October 02, 2025 at 02:00:40 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} v^{\prime }+v&={\mathrm e}^{-s} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 12

ode:=diff(v(s),s)+v(s) = exp(-s); 
dsolve(ode,v(s), singsol=all);
 

\[ v = \left (s +c_1 \right ) {\mathrm e}^{-s} \]

✓ Mathematica. Time used: 0.03 (sec). Leaf size: 15

ode=D[ v[s],s]+v[s]==Exp[-s]; 
ic={}; 
DSolve[{ode,ic},v[s],s,IncludeSingularSolutions->True]
 

\begin{align*} v(s)&\to e^{-s} (s+c_1) \end{align*}

✓ Sympy. Time used: 0.077 (sec). Leaf size: 8

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

\[ v{\left (s \right )} = \left (C_{1} + s\right ) e^{- s} \]