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$y = a e^{m x} + b e^{- m x}$ satisfies which of the following differential equations?

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dydx−my=0

dydx+my=0

d2ydx2+1n2y=0

d2ydx2−m2y=0

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detailed solution

Correct option is D

We have,y=aemx+be−mx⇒ dydx=maemx−mbe−mx⇒ d2ydx2=m2aemx+be−mx⇒ d2ydx2=m2y⇒d2ydx2−m2y=0

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y=aemx+be−mx satisfies which of the following differential equations?

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$y = a e^{m x} + b e^{- m x}$ satisfies which of the following differential equations?