46.6.12 problem 32

Internal problem ID [9633]
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. 7.3.1 TRANSLATION ON THE s-AXIS. Page 297
Problem number : 32
Date solved : Tuesday, September 30, 2025 at 06:21:39 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+8 y^{\prime }+20 y&=0 \end{align*}

Using Laplace method With initial conditions

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

✓ Maple. Time used: 0.099 (sec). Leaf size: 5

ode:=diff(diff(y(t),t),t)+8*diff(y(t),t)+20*y(t) = 0; 
ic:=[y(0) = 0, D(y)(Pi) = 0]; 
dsolve([ode,op(ic)],y(t),method='laplace');
 

\[ y = 0 \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 6

ode=D[y[t],{t,2}]+8*D[y[t],t]+20*y[t]==0; 
ic={y[0]==0,Derivative[1][y][Pi]==0}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to 0 \end{align*}

✓ Sympy. Time used: 0.112 (sec). Leaf size: 3

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(20*y(t) + 8*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {y(0): 0, Subs(Derivative(y(t), t), t, pi): 0} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = 0 \]