If `y=Acosn x+Bsinn x ,s howt h a t` `(d^2y)/(dx^2)+n^2y=0`

Explanation

To show that \(\frac{d^2y}{dx^2} + n^2y = 0\) for the function \(y = A \cos(nx) + B \sin(nx)\), we will follow these steps:

### Step 1: Differentiate \(y\) to find \(\frac{dy}{dx}\)
Given:
\[ y = A \cos(nx) + B \sin(nx) \]
We differentiate \(y\) with respect to \(x\):
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