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Solution for If Y = Ae2x + Be−X, Show That, D 2 Y D X 2 − D Y D X − 2 Y = 0 ? - CBSE (Commerce) Class 12 - Mathematics

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Question

If y = ae2x + be−x, show that, \[\frac{d^2 y}{d x^2} - \frac{dy}{dx} - 2y = 0\] ?

Solution

Here,

\[y = a e^{2x} + b e^{- x} \]

\[\text { Differentiating w . r . t . x, we get } \]

\[\frac{d y}{d x} = 2a e^{2x} - b e^{- x} \]

\[\text { Differentiating again w . r . t . x, we get }\]

\[\frac{d^2 y}{d x^2} = 4a e^{2x} + b e^{- x} \]

\[ \Rightarrow \frac{d^2 y}{d x^2} = 2a e^{2x} - b e^{- x} + 2\left( a e^{2x} + b e^{- x} \right)\]

\[ \Rightarrow \frac{d^2 y}{d x^2} = \frac{d y}{d x} + 2y \]

\[ \Rightarrow \frac{d^2 y}{d x^2} - \frac{d y}{d x} - 2y = 0\]

Hence proved.

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Solution for question: If Y = Ae2x + Be−X, Show That, D 2 Y D X 2 − D Y D X − 2 Y = 0 ? concept: Simple Problems on Applications of Derivatives. For the courses CBSE (Commerce), CBSE (Arts), PUC Karnataka Science, CBSE (Science)
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