Linear Second Order ODE/y'' - y = 0/Proof 3

Theorem

The second order ODE:

$(1): \quad y - y = 0$

has the general solution:

$y = C_1 e^x + C_2 e^{-x}$

Proof

This is an instance of:

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

which yields:

$y = C_1 e^{k x} + C_2 e^{-k x}$

where $k = 1$.

Hence the result.

$\blacksquare$