20.23.2 problem Problem 2

Internal problem ID [3974]
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 2
Date solved : Monday, January 27, 2025 at 08:05:31 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }-2 y&=\delta \left (t -2\right ) \end{align*}

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 2.973 (sec). Leaf size: 20

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

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

✓ Solution by Mathematica

Time used: 0.031 (sec). Leaf size: 23

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

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