15.18.2 problem 2

Internal problem ID [3245]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 35, page 157
Problem number : 2
Date solved : Monday, January 27, 2025 at 07:27:24 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }&=k^{2} y \end{align*}

✓ Solution by Maple

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

dsolve(diff(y(t),t$2)=k^2*y(t),y(t), singsol=all)
 

\[ y = c_{1} {\mathrm e}^{-k t}+c_2 \,{\mathrm e}^{k t} \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 23

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

\[ y(t)\to c_1 e^{k t}+c_2 e^{-k t} \]