52.8.1 problem 1

Internal problem ID [8365]
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 : 1
Date solved : Monday, January 27, 2025 at 03:49:37 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }-3 y&=\delta \left (t -2\right ) \end{align*}

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 0.698 (sec). Leaf size: 15

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

\[ y = \operatorname {Heaviside}\left (t -2\right ) {\mathrm e}^{3 t -6} \]

✓ Solution by Mathematica

Time used: 0.028 (sec). Leaf size: 17

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

\[ y(t)\to e^{3 t-6} \theta (t-2) \]