Internal problem ID [5229]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 2. Linear equations with constant coefficients. Page 83
Problem number: 1(a).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 13
dsolve(diff(y(x),x$2)+y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \sin \relax (x ) c_{1}+\cos \relax (x ) c_{2} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 16
DSolve[y''[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \cos (x)+c_2 \sin (x) \\ \end{align*}