Internal problem ID [8582]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1002.
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(diff(y(x),x),x)+y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \sin \relax (x )+c_{2} \cos \relax (x ) \]
✓ Solution by Mathematica
Time used: 0.003 (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*}