74.5.27 problem 27

Internal problem ID [15912]
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, March 13, 2025 at 06:57:09 AM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 12

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

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

✓ Mathematica. Time used: 0.05 (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]
 

\[ y(t)\to e^{-t} (t-1) \]

✓ Sympy. Time used: 0.138 (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)
 

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