If y = a sin x + (5 + 2x) cos x,then y'' + y | vedclass

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(D) Given: $y = a \sin x + (5 + 2x) \cos x$ . . . . . . $(i)$Differentiating with respect to $x$,we get:$y' = a \cos x + 2 \cos x - (5 + 2x) \sin x$$y

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$-4 \sin x$

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(D) Given: $y = a \sin x + (5 + 2x) \cos x$ . . . . . . $(i)$Differentiating with respect to $x$,we get:$y' = a \cos x + 2 \cos x - (5 + 2x) \sin x$$y' = (a + 2) \cos x - (5 + 2x) \sin x$Again differentiating with respect to $x$,we get:$y'' = -(a + 2) \sin x - 2 \sin x - (5 + 2x) \cos x$$y'' = -(a + 4) \sin x - (5 + 2x) \cos x$ . . . . . . $(ii)$Adding $(i)$ and $(ii)$,we get:$y'' + y = [-(a + 4) \sin x - (5 + 2x) \cos x] + [a \sin x + (5 + 2x) \cos x]$$y'' + y = -a \sin x - 4 \sin x - (5 + 2x) \cos x + a \sin x + (5 + 2x) \cos x$$y'' + y = -4 \sin x$.

If $y = a \sin x + (5 + 2x) \cos x$,then $y'' + y =$

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