80.6.1 problem 1

Internal problem ID [18565]
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 : Tuesday, January 28, 2025 at 12:00:14 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

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

dsolve(diff(theta(t),t$2)=-p^2*theta(t),theta(t), singsol=all)
 

\[ \theta = c_{1} \sin \left (p t \right )+c_{2} \cos \left (p t \right ) \]

✓ Solution by Mathematica

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

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

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