46.8.1 problem 1

Internal problem ID [9651]
Book : DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL, WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th edition.
Section : CHAPTER 7 THE LAPLACE TRANSFORM. EXERCISES 7.5. Page 315
Problem number : 1
Date solved : Tuesday, September 30, 2025 at 06:21:53 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }-3 y&=\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: 15

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

\[ y = \operatorname {Heaviside}\left (t -2\right ) {\mathrm e}^{3 t -6} \]

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 27

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

\begin{align*} y(t)&\to e^{3 t} \int _0^t\frac {\delta (K[1]-2)}{e^6}dK[1] \end{align*}

✓ Sympy. Time used: 0.401 (sec). Leaf size: 49

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

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