If y=a x^(n+1)+b x^(-n),t h e nx^2(d^2y)...

If `y=a x^(n+1)+b x^(-n),t h e nx^2(d^2y)/(dx^2)` is equal to (a) `n(n-1)y` (b) `n(n+1)y` (c) `n y` (d) `n^2y`

A

`m^(2)(ae^(mx)-be^(-mx))`

B

1

C

0

D

none of these

Text Solution

Verified by Experts

`y=ae^(mx)+be^(-mx)`
`therefore" "(dy)/(dx)=ame^(mx)-mbe^(-mx)`
`"Again "(d^(2)y)/(dx^(2))=am^(2)e^(mx)+m^(2)be^(-mx)`
`=m^(2)(ae^(mx)+be^(-mx))=m^(2)y`
`"or "(d^(2)y)/dx^(2)-m^(2)y=0`

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