74.5.27 problem 27

Internal problem ID [15991]
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 : Tuesday, January 28, 2025 at 08:25:52 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*}

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

Time used: 0.050 (sec). Leaf size: 14

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

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