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

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

has the solution:
 * $y = A \sin \left({k x + B}\right)$

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

Proof
Using Solution of Second Order Differential Equation with Missing Independent Variable, $(1)$ can be expressed as:

From Multiple of Sine plus Multiple of Cosine: Sine Form, this can be expressed as:


 * $y = C_1 \sin k x + C_2 \cos k x$