If y=a sin x+(5+2 x) cos x,then y^{prime prim | vedclass

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(D) Given $y=a \sin x+(5+2 x) \cos x$. Differentiating with respect to $x$ using the product rule: $y^{\prime} = a \cos x + (5+2x)(-\sin x) + (2)\cos

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$-4 \sin x$

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(D) Given $y=a \sin x+(5+2 x) \cos x$. Differentiating with respect to $x$ using the product rule: $y^{\prime} = a \cos x + (5+2x)(-\sin x) + (2)\cos x$ $y^{\prime} = a \cos x - (5+2x)\sin x + 2 \cos x$. Differentiating again with respect to $x$: $y^{\prime \prime} = -a \sin x - [(5+2x)\cos x + (2)\sin x] - 2 \sin x$ $y^{\prime \prime} = -a \sin x - (5+2x)\cos x - 2 \sin x - 2 \sin x$ $y^{\prime \prime} = -(a \sin x + (5+2x)\cos x) - 4 \sin x$ Since $y = a \sin x + (5+2x)\cos x$,we substitute $y$ into the equation: $y^{\prime \prime} = -y - 4 \sin x$ Therefore,$y^{\prime \prime} + y = -4 \sin x$.

If $y=a \sin x+(5+2 x) \cos x$,then $y^{\prime \prime}+y=$

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