If `y=A e^(-k t)cos(p t+c),` then prove that `(d^2y)/(dt^2)+2k(dy)/(dx)+n^2y=0` , where `n^2=p^2+k^2`

Explanation

`y=A e^{-k t} cos (p t+c) ldots(i)`
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frac{d y}{d t}=-A k e^{-k t} cos (p t+c)-A p e^{-k t} sin (p t+c) quad ldots text { (ii) }`
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frac{d^{2} y}{d t^{2}}=A k^{2} e^{-k t} cos (p t+c)+A p k e^{-k t} sin (p t
+c)+A p k e^{-k t} sin (p t+c)-A p^{2} e^{-k t} cos (p t+c) `
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