52.8.2 problem 2

Internal problem ID [8366]
Book : DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL, WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th edition.
Section : CHAPTER 7 THE LAPLACE TRANSFORM. EXERCISES 7.5. Page 315
Problem number : 2
Date solved : Monday, January 27, 2025 at 03:49:38 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+y&=\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: 0.667 (sec). Leaf size: 22

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

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

✓ Solution by Mathematica

Time used: 0.028 (sec). Leaf size: 19

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

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