`y=ae^(mx)+b^(-mx)` satisfies which of the following differential equation?

Options

A. `(dy)/(dx)+my=0`
B. `(dy)/(dx)-my=0`
C. `(d^(2)y)/(dx^(2))-m^(2)y=0`
D. `(d^(2)y)/(dx^(2))+m^(2)y=0`

Explanation

To determine which differential equation is satisfied by the function \( y = ae^{mx} + be^{-mx} \), we will follow these steps:

### Step 1: Differentiate \( y \) to find \( \frac{dy}{dx} \)

Given:
\[ y = ae^{mx} + be^{-mx} \]
...