80.8.4 problem 4

Internal problem ID [18583]
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 : 4
Date solved : Tuesday, January 28, 2025 at 12:02:56 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} r^{\prime \prime }-a^{2} r&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 18

dsolve(diff(r(phi),phi$2)-a^2*r(phi)=0,r(phi), singsol=all)
 

\[ r = c_{1} {\mathrm e}^{-a \phi }+c_{2} {\mathrm e}^{a \phi } \]

✓ Solution by Mathematica

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

DSolve[D[r[phi],{phi,2}]-a^2*r[phi]==0,r[phi],phi,IncludeSingularSolutions -> True]
 

\[ r(\phi )\to c_1 e^{a \phi }+c_2 e^{-a \phi } \]