49.23.4 problem 1(d)

Internal problem ID [7762]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 6. Existence and uniqueness of solutions to systems and nth order equations. Page 238
Problem number : 1(d)
Date solved : Monday, January 27, 2025 at 03:12:13 PM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

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

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

\[ y = c_{1} \sin \left (k x \right )+c_{2} \cos \left (k x \right ) \]

✓ Solution by Mathematica

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

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

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