For n in N,if y = a x^{n+1} + b x^{-n},then x | vedclass

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(B) Given $y = a x^{n+1} + b x^{-n}$.First derivative: $\frac{dy}{dx} = a(n+1)x^n + b(-n)x^{-n-1}$.Second derivative: $\frac{d^2y}{dx^2} = a(n+1)nx^{n

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$n(n+1) y$

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(B) Given $y = a x^{n+1} + b x^{-n}$.First derivative: $\frac{dy}{dx} = a(n+1)x^n + b(-n)x^{-n-1}$.Second derivative: $\frac{d^2y}{dx^2} = a(n+1)nx^{n-1} + b(-n)(-n-1)x^{-n-2}$.$\frac{d^2y}{dx^2} = an(n+1)x^{n-1} + bn(n+1)x^{-n-2}$.Multiply by $x^2$: $x^2 \frac{d^2y}{dx^2} = an(n+1)x^{n+1} + bn(n+1)x^{-n}$.$x^2 \frac{d^2y}{dx^2} = n(n+1) [a x^{n+1} + b x^{-n}]$.Since $y = a x^{n+1} + b x^{-n}$,we have $x^2 \frac{d^2y}{dx^2} = n(n+1)y$.

For $n \in N$,if $y = a x^{n+1} + b x^{-n}$,then $x^2 \frac{d^2 y}{d x^2} = $

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