Linear Second Order ODE/y'' + 4 y = 0/Proof 2

Theorem

The second order ODE:

$(1): \quad y + 4 y = 0$

has the general solution:

$y = C_1 \cos 2 x + C_2 \sin 2 x$

Proof

This is an instance of:

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

which yields:

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

where $k = 2$.

Hence the result.

$\blacksquare$