80.6.1 problem 1

Internal problem ID [18494]
Book : Elementary Differential Equations. By Thornton C. Fry. D Van Nostrand. NY. First Edition (1929)
Section : Chapter IV. Methods of solution: First order equations. section 33. Problems at page 91
Problem number : 1
Date solved : Monday, March 31, 2025 at 05:37:36 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} \theta ^{\prime \prime }&=-p^{2} \theta \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 17

ode:=diff(diff(theta(t),t),t) = -p^2*theta(t); 
dsolve(ode,theta(t), singsol=all);
 

\[ \theta = c_1 \sin \left (p t \right )+c_2 \cos \left (p t \right ) \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 20

ode=D[theta[t],{t,2}]==-p^2*theta[t]; 
ic={}; 
DSolve[{ode,ic},theta[t],t,IncludeSingularSolutions->True]
 

\[ \theta (t)\to c_1 \cos (p t)+c_2 \sin (p t) \]

✓ Sympy. Time used: 0.093 (sec). Leaf size: 19

from sympy import * 
t = symbols("t") 
p = symbols("p") 
theta = Function("theta") 
ode = Eq(p**2*theta(t) + Derivative(theta(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=theta(t),ics=ics)
 

\[ \theta {\left (t \right )} = C_{1} e^{- i p t} + C_{2} e^{i p t} \]