74.11.53 problem 62 (d)

Internal problem ID [16303]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.3, page 156
Problem number : 62 (d)
Date solved : Tuesday, January 28, 2025 at 09:02:12 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+4 y&={\mathrm e}^{-4 t} \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 12

dsolve([diff(y(t),t)+4*y(t)=exp(-4*t),y(0) = 1],y(t), singsol=all)
 

\[ y = \left (t +1\right ) {\mathrm e}^{-4 t} \]

✓ Solution by Mathematica

Time used: 0.055 (sec). Leaf size: 14

DSolve[{D[y[t],t]+4*y[t]==Exp[-4*t],{y[0]==1}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-4 t} (t+1) \]