For y=7 sin x+5 cos x,if frac{d^2 y}{d x^2}-m | vedclass

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Question

(C) Given the equation $y = 7 \sin x + 5 \cos x$. First,find the first derivative with respect to $x$: $\frac{dy}{dx} = \frac{d}{dx}(7 \sin x + 5 \cos

Vedclass · Accepted Answer

$-1$

Vedclass · Answer

(C) Given the equation $y = 7 \sin x + 5 \cos x$. First,find the first derivative with respect to $x$: $\frac{dy}{dx} = \frac{d}{dx}(7 \sin x + 5 \cos x) = 7 \cos x - 5 \sin x$. Next,find the second derivative with respect to $x$: $\frac{d^2y}{dx^2} = \frac{d}{dx}(7 \cos x - 5 \sin x) = -7 \sin x - 5 \cos x$. Factor out $-1$ from the expression: $\frac{d^2y}{dx^2} = -(7 \sin x + 5 \cos x)$. Since $y = 7 \sin x + 5 \cos x$,we can substitute $y$ into the equation: $\frac{d^2y}{dx^2} = -y$. Rearranging gives $\frac{d^2y}{dx^2} + y = 0$. Comparing this with the given equation $\frac{d^2y}{dx^2} - my = 0$,we have $-m = 1$,which implies $m = -1$. Therefore,the correct option is $C$.

For $y=7 \sin x+5 \cos x$,if $\frac{d^2 y}{d x^2}-m y=0$,then $m=$ . . . . . .

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