86.8.10 problem 10

Internal problem ID [23170]
Book : An introduction to Differential Equations. By Howard Frederick Cleaves. 1969. Oliver and Boyd publisher. ISBN 0050015044
Section : Chapter 5. Linear equations of the second order with constant coefficients. Exercise 5e at page 91
Problem number : 10
Date solved : Thursday, October 02, 2025 at 09:23:44 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 )&=0 \\ \end{align*}

✓ Maple. Time used: 0.011 (sec). Leaf size: 10

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

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

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 11

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

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

✓ Sympy. Time used: 0.035 (sec). Leaf size: 8

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): 0} 
dsolve(ode,func=s(t),ics=ics)
 

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