74.6.2 problem 2 (eq 39)

Internal problem ID [19852]
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 : 2 (eq 39)
Date solved : Thursday, October 02, 2025 at 04:48:32 PM
CAS classification : [_quadrature]

\begin{align*} \sec \left (\theta \right )^{2}&=\frac {m s^{\prime }}{k} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 13

ode:=sec(theta)^2 = m/k*diff(s(theta),theta); 
dsolve(ode,s(theta), singsol=all);
 

\[ s = \frac {k \tan \left (\theta \right )}{m}+c_1 \]

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 15

ode=Sec[theta]^2==m/k*D[s[theta],theta]; 
ic={}; 
DSolve[{ode,ic},s[theta],theta,IncludeSingularSolutions->True]
 

\begin{align*} s(\theta )&\to \frac {k \tan (\theta )}{m}+c_1 \end{align*}

✓ Sympy. Time used: 0.096 (sec). Leaf size: 14

from sympy import * 
theta = symbols("theta") 
k = symbols("k") 
m = symbols("m") 
s = Function("s") 
ode = Eq(cos(theta)**(-2) - m*Derivative(s(theta), theta)/k,0) 
ics = {} 
dsolve(ode,func=s(theta),ics=ics)
 

\[ s{\left (\theta \right )} = C_{1} + \frac {k \sin {\left (\theta \right )}}{m \cos {\left (\theta \right )}} \]