If $y = a sin (5 x + c)$ , then

\frac{d y}{d x} = 5 y

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\frac{d y}{d x} = - 5 y

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\frac{d^{2} y}{d x^{2}} = - 25 y

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\frac{d^{2} y}{d x^{2}} = 25 y

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Solution

The correct option is C $\frac{d^{2} y}{d x^{2}} = - 25 y$
Given,
$y = a sin (5 x + c)$

On differentiating with respect to $x$ , we get
$\frac{d y}{d x} = 5 a cos (5 x + c)$

On again differentiating with respect to $x$ , we get
$\frac{d^{2} y}{d x^{2}} = - 25 a sin (5 x + c)$
$= - 25 y$

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