`If y=int_0^xf(t)sin{k(x-t)}dt, then prove that ((dt^2y)/(dx^2))+k^2y=kf(x)`

Explanation

To prove that \(\frac{d^2y}{dx^2} + k^2y = kf(x)\) given that \(y = \int_0^x f(t) \sin(k(x - t)) dt\), we will follow a systematic approach.

### Step 1: Write down the expression for \(y\)
We start with the given expression:
\[ y = \int_0^x f(t) \sin(k(x - t)) dt \]

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