73.22.8 problem 31.7 (a)

Internal problem ID [15635]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 31. Delta Functions. Additional Exercises. page 572
Problem number : 31.7 (a)
Date solved : Tuesday, January 28, 2025 at 08:03:26 AM
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 )&=2 \end{align*}

✓ Solution by Maple

Time used: 8.073 (sec). Leaf size: 22

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

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

✓ Solution by Mathematica

Time used: 0.028 (sec). Leaf size: 29

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

\[ y(t)\to e^{-3 t} \left (\int _0^te^6 \delta (K[1]-2)dK[1]+2\right ) \]