67.19.4 problem 28.8 (a)

Internal problem ID [16889]
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 (a)
Date solved : Thursday, October 02, 2025 at 01:40:08 PM
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: 0.102 (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,op(ic)],y(t),method='laplace');
 

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

✓ Mathematica. Time used: 0.01 (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]
 

\begin{align*} y(t)&\to 3 e^{4 t} \cos (t) \end{align*}

✓ Sympy. Time used: 0.103 (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)
 

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