74.8.1 problem 1 (eq 100)

Internal problem ID [19866]
Book : Elementary Differential Equations. By Thornton C. Fry. D Van Nostrand. NY. First Edition (1929)
Section : Chapter VII. Linear equations of order higher than the first. section 56. Problems at page 163
Problem number : 1 (eq 100)
Date solved : Thursday, October 02, 2025 at 04:59:58 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} \theta ^{\prime \prime }-p^{2} \theta &=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 18

ode:=diff(diff(theta(x),x),x)-p^2*theta(x) = 0; 
dsolve(ode,theta(x), singsol=all);
 

\[ \theta = c_1 \,{\mathrm e}^{-p x}+c_2 \,{\mathrm e}^{p x} \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 23

ode=D[theta[x],{x,2}]-p^2*theta[x]==0; 
ic={}; 
DSolve[{ode,ic},theta[x],x,IncludeSingularSolutions->True]
 

\begin{align*} \theta (x)&\to c_1 e^{p x}+c_2 e^{-p x} \end{align*}

✓ Sympy. Time used: 0.045 (sec). Leaf size: 15

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

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