If $y = a x^{n + 1} + b x^{- n}$ then $x^{2} y^{''} =$

n y

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(n + 1) y

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- n (n + 1) y

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n (n + 1) y

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Solution

The correct option is D $n (n + 1) y$
$y^{'} = (n + 1) a x^{n} - n b x^{- n - 1}$
$y^{''} = n (n + 1) a x^{n - 1} + n (n + 1) b x^{- n - 2}$
$x^{2} y^{''}$ $= n (n + 1) a x^{n + 1} + n (n + 1) b x^{- n} = n (n + 1) (a x^{n + 1} + b x^{- n}) = n (n + 1) y$

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