85.40.9 problem 2 (c)

Internal problem ID [22766]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 4. Linear differential equations. A Exercises at page 177
Problem number : 2 (c)
Date solved : Thursday, October 02, 2025 at 09:14:26 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} s^{\prime \prime }+16 s^{\prime }+64 s&=0 \end{align*}

With initial conditions

\begin{align*} s \left (0\right )&=0 \\ s^{\prime }\left (0\right )&=-4 \\ \end{align*}

✓ Maple. Time used: 0.011 (sec). Leaf size: 11

ode:=diff(diff(s(t),t),t)+16*diff(s(t),t)+64*s(t) = 0; 
ic:=[s(0) = 0, D(s)(0) = -4]; 
dsolve([ode,op(ic)],s(t), singsol=all);
 

\[ s = -4 \,{\mathrm e}^{-8 t} t \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 13

ode=D[s[t],{t,2}]+16*D[s[t],{t,1}]+64*s[t]==0; 
ic={s[0]==0,Derivative[1][s][0] ==-4}; 
DSolve[{ode,ic},s[t],t,IncludeSingularSolutions->True]
 

\begin{align*} s(t)&\to -4 e^{-8 t} t \end{align*}

✗ Sympy

from sympy import * 
t = symbols("t") 
s = Function("s") 
ode = Eq(64*s(t) + 16*Derivative(s(t), t) + Derivative(s(t), (t, 2)),0) 
ics = {s(0): 0, Subs(Derivative(s(t), t), x, -4): 0} 
dsolve(ode,func=s(t),ics=ics)
 

ValueError : Invalid boundary conditions for Derivatives