73.22.1 problem 31.6 (a)

Internal problem ID [15628]
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 (a)
Date solved : Tuesday, January 28, 2025 at 08:03:20 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=3 \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: 9.498 (sec). Leaf size: 10

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

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

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 19

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

\[ y(t)\to \int _0^t3 \delta (K[1]-2)dK[1] \]