Internal problem ID [5341]
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).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+k^{2} y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 17
dsolve(diff(y(x),x$2)+k^2*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \sin \left (k x \right )+c_{2} \cos \left (k x \right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 20
DSolve[y''[x]+k^2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \cos (k x)+c_2 \sin (k x) \\ \end{align*}