73.22.2 problem 31.6 (b)

Internal problem ID [15550]
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 : Thursday, March 13, 2025 at 06:11:19 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*}

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

ode:=diff(y(t),t) = Dirac(t-2)-Dirac(t-4); 
ic:=y(0) = 0; 
dsolve([ode,ic],y(t),method='laplace');
 

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

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

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

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

✓ Sympy. Time used: 0.235 (sec). Leaf size: 29

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(Dirac(t - 4) - Dirac(t - 2) + Derivative(y(t), t),0) 
ics = {y(0): 0} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \int \left (- \operatorname {Dirac}{\left (t - 4 \right )} + \operatorname {Dirac}{\left (t - 2 \right )}\right )\, dt - \int \limits ^{0} \left (- \operatorname {Dirac}{\left (t - 4 \right )}\right )\, dt - \int \limits ^{0} \operatorname {Dirac}{\left (t - 2 \right )}\, dt \]