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

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

has the general solution:
 * $y = A \, \map \sin {k x + B}$

or can be expressed as:
 * $y = C_1 \sin k x + C_2 \cos k x$

Also see

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