20.23.1 problem Problem 1

Internal problem ID [3973]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 10, The Laplace Transform and Some Elementary Applications. Exercises for 10.8. page 710
Problem number : Problem 1
Date solved : Monday, January 27, 2025 at 08:05:30 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+y&=\delta \left (t -5\right ) \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=3 \end{align*}

✓ Solution by Maple

Time used: 3.096 (sec). Leaf size: 22

dsolve([diff(y(t),t)+y(t)=Dirac(t-5),y(0) = 3],y(t), singsol=all)
 

\[ y = \operatorname {Heaviside}\left (t -5\right ) {\mathrm e}^{-t +5}+3 \,{\mathrm e}^{-t} \]

✓ Solution by Mathematica

Time used: 0.032 (sec). Leaf size: 21

DSolve[{D[y[t],t]+y[t]==DiracDelta[t-5],{y[0]==3}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-t} \left (e^5 \theta (t-5)+3\right ) \]