Linear Second Order ODE/y'' - 4 y = 0/Proof 2
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Theorem
The second order ODE:
- $(1): \quad y - 4 y = 0$
has the general solution:
- $y = C_1 e^{2 x} + C_2 e^{-2 x}$
Proof
This is an instance of:
which yields:
- $y = C_1 e^{k x} + C_2 e^{-k x}$
where $k = 2$.
Hence the result.
$\blacksquare$