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If y=500\ e^(7x)+600\ e^(-7x) , show tha...

If `y=500\ e^(7x)+600\ e^(-7x)` , show that `(d^2y)/(dx^2)=49\ y` .

A

y

B

7y

C

40y

D

49 y

Text Solution

Verified by Experts

The correct Answer is:
D
Given , ` y = 500 e^(7x) + 600 e^(-7x). (-7)` …(i)
On differentiating twice w.r.t.x, we get
`(dy)/(dx) = (7xx500 )e^(7x) . -7 (7 xx 600)_(e)^(-7x) (-7)`
` 49 { 500 e^(7x) + 600 e ^(-7x)} `
` rArr (d^(2) y)/(dx^(2)) = 49 y ` .
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