73.22.2 problem 31.6 (b)

Internal problem ID [15629]
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 (b)
Date solved : Tuesday, January 28, 2025 at 08:03:21 AM
CAS classification : [_quadrature]

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

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 9.367 (sec). Leaf size: 15

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

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

✓ Solution by Mathematica

Time used: 0.009 (sec). Leaf size: 25

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

\[ y(t)\to \int _0^t(\delta (K[1]-2)-\delta (K[1]-4))dK[1] \]