80.8.1 problem 1 (eq 100)

Internal problem ID [18580]
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 : Tuesday, January 28, 2025 at 12:02:49 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 18

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

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

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 23

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

\[ \theta (x)\to c_1 e^{p x}+c_2 e^{-p x} \]