73.22.5 problem 31.6 (e)

Internal problem ID [15632]
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 : 31.6 (e)
Date solved : Tuesday, January 28, 2025 at 08:03:23 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+2 y&=4 \delta \left (t -1\right ) \end{align*}

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 9.559 (sec). Leaf size: 16

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

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

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 28

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

\[ y(t)\to e^{-2 t} \int _0^t4 e^2 \delta (K[1]-1)dK[1] \]