73.19.7 problem 28.8 (d)

Internal problem ID [15526]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 28. The inverse Laplace transform. Additional Exercises. page 509
Problem number : 28.8 (d)
Date solved : Thursday, March 13, 2025 at 06:10:54 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+8 y^{\prime }+17 y&=0 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=-12 \end{align*}

✓ Maple. Time used: 8.731 (sec). Leaf size: 12

ode:=diff(diff(y(t),t),t)+8*diff(y(t),t)+17*y(t) = 0; 
ic:=y(0) = 3, D(y)(0) = -12; 
dsolve([ode,ic],y(t),method='laplace');
 

\[ y = 3 \,{\mathrm e}^{-4 t} \cos \left (t \right ) \]

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 14

ode=D[y[t],{t,2}]+8*D[y[t],t]+17*y[t]==0; 
ic={y[0]==3,Derivative[1][y][0] ==-12}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to 3 e^{-4 t} \cos (t) \]

✓ Sympy. Time used: 0.190 (sec). Leaf size: 12

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(17*y(t) + 8*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {y(0): 3, Subs(Derivative(y(t), t), t, 0): -12} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = 3 e^{- 4 t} \cos {\left (t \right )} \]