Linear Second Order ODE/y'' - k^2 y = 0

Theorem
The second order ODE:
 * $(1): \quad y'' - k^2 y = 0$

has the solution:
 * $y = C_1 e^{k x} + C_2 e^{-k x}$

Also see

 * Second Order ODE: $y'' + k^2 y = 0$