If 500e7x-600e-7x- show that d 2 y d x 2 -49y

Given, 500 e^7x+600 e^ 7x On differentiating w.r.t. x , we get dydx=7× 500e^7x 7× 600e^ 7x Again differentiating w.r.t. x , d ^ 2 y d x ...

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Definition of Function

If 500e7x+6...

Question

If $500 e^{7 x} + 600 e^{- 7 x}$ , show that $\frac{d^{2} y}{d x^{2}} = 49 y$

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Solution

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y = 500 e^{7 x} + 600 e^{- 7 x}

\frac{d^{2} y}{d x^{2}} = 49 y

$I f y = 500 e^{7 x} + 600 e^{- 7 x}, s h o w t h a t \frac{d^{2} y}{d x^{2}} = 49 y .$

\frac{d^{2} y}{d x^{2}} = 49 y

y = 500 e^{7 x} + 600 e^{- 7 x},

\frac{d^{2} y}{d x^{2}} - 49 y

e^{y} (x + 1) = 1

\frac{d^{2} y}{d x^{2}} = {(\frac{d y}{d x})}^{2}

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