68.5.2 problem 2

Internal problem ID [17253]
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 : 2
Date solved : Thursday, October 02, 2025 at 01:59:57 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} -y+y^{\prime }&=2 \,{\mathrm e}^{-t} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 15

ode:=diff(y(t),t)-y(t) = 2*exp(-t); 
dsolve(ode,y(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.033 (sec). Leaf size: 19

ode=D[y[t],t]-y[t]==2*Exp[-t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.074 (sec). Leaf size: 12

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-y(t) + Derivative(y(t), t) - 2*exp(-t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

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