If `y=e^(-x)(A cos x + B sin x)` then y is a situation of

Options

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

Explanation

To determine if \( y = e^{-x}(A \cos x + B \sin x) \) is a solution of a differential equation, we will differentiate \( y \) twice and then express the results in terms of \( y \) and its derivatives.

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

Given:
\[ y = e^{-x}(A \cos x + B \sin x) \]
...