85.1.10 problem 5 (c)

Internal problem ID [22415]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 1. Differential equations in general. A Exercises at page 12
Problem number : 5 (c)
Date solved : Thursday, October 02, 2025 at 08:38:40 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} s^{\prime \prime }&=-9 s \end{align*}

With initial conditions

\begin{align*} s \left (0\right )&=9 \\ s^{\prime }\left (0\right )&=18 \\ \end{align*}

✓ Maple. Time used: 0.012 (sec). Leaf size: 17

ode:=diff(diff(s(t),t),t) = -9*s(t); 
ic:=[s(0) = 9, D(s)(0) = 18]; 
dsolve([ode,op(ic)],s(t), singsol=all);
 

\[ s = 6 \sin \left (3 t \right )+9 \cos \left (3 t \right ) \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 18

ode=D[s[t],{t,2}]==-9*s[t]; 
ic={s[0]==9,Derivative[1][s][0] ==18}; 
DSolve[{ode,ic},s[t],t,IncludeSingularSolutions->True]
 

\begin{align*} s(t)&\to 6 \sin (3 t)+9 \cos (3 t) \end{align*}

✓ Sympy. Time used: 0.034 (sec). Leaf size: 15

from sympy import * 
t = symbols("t") 
s = Function("s") 
ode = Eq(9*s(t) + Derivative(s(t), (t, 2)),0) 
ics = {s(0): 9, Subs(Derivative(s(t), t), t, 0): 18} 
dsolve(ode,func=s(t),ics=ics)
 

\[ s{\left (t \right )} = 6 \sin {\left (3 t \right )} + 9 \cos {\left (3 t \right )} \]