15.18.3 problem 3

Internal problem ID [3246]
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 : 3
Date solved : Monday, January 27, 2025 at 07:27:27 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} x^{\prime \prime }+k^{2} x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 17

dsolve(diff(x(t),t$2)+k^2*x(t)=0,x(t), singsol=all)
 

\[ x = c_{1} \sin \left (k t \right )+c_2 \cos \left (k t \right ) \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 20

DSolve[D[x[t],{t,2}]+k^2*x[t]==0,x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to c_1 \cos (k t)+c_2 \sin (k t) \]