80.6.2 problem 2 (eq 39)

Internal problem ID [18566]
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 : Tuesday, January 28, 2025 at 12:00:16 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 13

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

\[ s \left (\theta \right ) = \frac {k \tan \left (\theta \right )}{m}+c_{1} \]

✓ Solution by Mathematica

Time used: 0.010 (sec). Leaf size: 15

DSolve[Sec[theta]^2==m/k*D[s[theta],theta],s[theta],theta,IncludeSingularSolutions -> True]
 

\[ s(\theta )\to \frac {k \tan (\theta )}{m}+c_1 \]