20.23.3 problem Problem 3

Internal problem ID [3975]
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 3
Date solved : Monday, January 27, 2025 at 08:05:31 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+4 y&=3 \delta \left (t -1\right ) \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 3.341 (sec). Leaf size: 23

dsolve([diff(y(t),t)+4*y(t)=3*Dirac(t-1),y(0) = 2],y(t), singsol=all)
 

\[ y = 3 \operatorname {Heaviside}\left (-1+t \right ) {\mathrm e}^{-4 t +4}+2 \,{\mathrm e}^{-4 t} \]

✓ Solution by Mathematica

Time used: 0.031 (sec). Leaf size: 22

DSolve[{D[y[t],t]+4*y[t]==3*DiracDelta[t-1],{y[0]==2}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-4 t} \left (3 e^4 \theta (t-1)+2\right ) \]