If y = 100 e^{2x} + 200 e^{-2x} and frac{d^2 | vedclass

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(D) Given the equation $y = 100 e^{2x} + 200 e^{-2x}$.First,find the first derivative $\frac{dy}{dx}$:$\frac{dy}{dx} = 100 \cdot 2 e^{2x} + 200 \cdot

Vedclass · Accepted Answer

$4$

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(D) Given the equation $y = 100 e^{2x} + 200 e^{-2x}$.First,find the first derivative $\frac{dy}{dx}$:$\frac{dy}{dx} = 100 \cdot 2 e^{2x} + 200 \cdot (-2) e^{-2x} = 200 e^{2x} - 400 e^{-2x}$.Next,find the second derivative $\frac{d^2 y}{dx^2}$:$\frac{d^2 y}{dx^2} = 200 \cdot 2 e^{2x} - 400 \cdot (-2) e^{-2x} = 400 e^{2x} + 800 e^{-2x}$.Factor out $4$ from the expression:$\frac{d^2 y}{dx^2} = 4(100 e^{2x} + 200 e^{-2x})$.Since $y = 100 e^{2x} + 200 e^{-2x}$,we can substitute $y$ into the equation:$\frac{d^2 y}{dx^2} = 4y$.Comparing this with $\frac{d^2 y}{dx^2} = ay$,we get $a = 4$.

If $y = 100 e^{2x} + 200 e^{-2x}$ and $\frac{d^2 y}{dx^2} = ay$,then $a = $ . . . . . .

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