68.5.27 problem 27

Internal problem ID [17278]
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 : 27
Date solved : Thursday, October 02, 2025 at 02:00:42 PM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

\begin{align*} y \left (0\right )&=-1 \\ \end{align*}

✓ Maple. Time used: 0.025 (sec). Leaf size: 12

ode:=diff(y(t),t)+y(t) = exp(-t); 
ic:=[y(0) = -1]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.029 (sec). Leaf size: 14

ode=D[y[t],t]+y[t]==Exp[-t]; 
ic={y[0]==-1}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to e^{-t} (t-1) \end{align*}

✓ Sympy. Time used: 0.078 (sec). Leaf size: 8

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(y(t) + Derivative(y(t), t) - exp(-t),0) 
ics = {y(0): -1} 
dsolve(ode,func=y(t),ics=ics)
 

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