46.8.14 problem 15(b)

Internal problem ID [9664]
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 : 15(b)
Date solved : Tuesday, September 30, 2025 at 06:22:03 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+10 y&=\delta \left (t \right ) \end{align*}

Using Laplace method

✓ Maple. Time used: 0.087 (sec). Leaf size: 30

ode:=diff(diff(y(t),t),t)+2*diff(y(t),t)+10*y(t) = Dirac(t); 
dsolve(ode,y(t),method='laplace');
 

\[ y = \frac {{\mathrm e}^{-t} \left (3 y \left (0\right ) \cos \left (3 t \right )+\sin \left (3 t \right ) \left (y^{\prime }\left (0\right )+y \left (0\right )+1\right )\right )}{3} \]

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 51

ode=D[y[t],{t,2}]+2*D[y[t],t]+10*y[t]==DiracDelta[t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to e^{-t} \sin (3 t) \int _1^t\frac {\delta (K[1])}{3}dK[1]+e^{-t} (c_2 \cos (3 t)+c_1 \sin (3 t)) \end{align*}

✓ Sympy. Time used: 2.336 (sec). Leaf size: 49

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-Dirac(t) + 10*y(t) + 2*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \left (\left (C_{1} - \frac {\int \operatorname {Dirac}{\left (t \right )} e^{t} \sin {\left (3 t \right )}\, dt}{3}\right ) \cos {\left (3 t \right )} + \left (C_{2} + \frac {\int \operatorname {Dirac}{\left (t \right )} e^{t} \cos {\left (3 t \right )}\, dt}{3}\right ) \sin {\left (3 t \right )}\right ) e^{- t} \]