If $y = e^{2 x} + e^{- 2 x}$ and $\frac{d^2y}{dx^2} = ky$, what is $k$?

Explanation

1. 01

   $\frac{dy}{dx} = 2 e^{2 x} - 2 e^{- 2 x}$.

2. 02

   $\frac{d^2y}{dx^2} = 4 \left(e^{4 x} + 1\right) e^{- 2 x}$, which is $4y$.