67.22.1 problem 31.6 (a)

Internal problem ID [16915]
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 : Thursday, October 02, 2025 at 01:40:20 PM
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*}

✓ Maple. Time used: 0.096 (sec). Leaf size: 10

ode:=diff(y(t),t) = 3*Dirac(t-2); 
ic:=[y(0) = 0]; 
dsolve([ode,op(ic)],y(t),method='laplace');
 

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

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

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

\begin{align*} y(t)&\to \int _0^t3 \delta (K[1]-2)dK[1] \end{align*}

✓ Sympy. Time used: 0.125 (sec). Leaf size: 19

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-3*Dirac(t - 2) + Derivative(y(t), t),0) 
ics = {y(0): 0} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = 3 \int \operatorname {Dirac}{\left (t - 2 \right )}\, dt - 3 \int \limits ^{0} \operatorname {Dirac}{\left (t - 2 \right )}\, dt \]