y = 4sin 3x is a solution of the differential | vedclass

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(C) Given the function $y = 4\sin 3x$. Differentiating with respect to $x$,we get: $\frac{dy}{dx} = 4 	imes 3 \cos 3x = 12 \cos 3x$. Differentiating

Vedclass · Accepted Answer

$\frac{d^2y}{dx^2} + 9y = 0$

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(C) Given the function $y = 4\sin 3x$. Differentiating with respect to $x$,we get: $\frac{dy}{dx} = 4 	imes 3 \cos 3x = 12 \cos 3x$. Differentiating again with respect to $x$,we get: $\frac{d^2y}{dx^2} = 12 	imes (-3 \sin 3x) = -36 \sin 3x$. We can rewrite this as: $\frac{d^2y}{dx^2} = -9(4 \sin 3x)$. Since $y = 4 \sin 3x$,we substitute $y$ into the equation: $\frac{d^2y}{dx^2} = -9y$. Rearranging the terms,we get: $\frac{d^2y}{dx^2} + 9y = 0$. Thus,the correct option is $C$.

$y = 4\sin 3x$ is a solution of the differential equation

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