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If y=a\ x^(n+1)+b x^(-n) and x^2(d^2y)/(...

If `y=a\ x^(n+1)+b x^(-n)` and `x^2(d^2y)/(dx^2)=lambday` , then write the value of `lambda` .

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`y=a x^{n+1}+b x^{-n}`
` frac{d y}{d x}=(n+1) a x^{n}+(-n) b x^{-n-1}`
` frac{d^{2} y}{d x^{2}}=n(n+1) a x^{n-1}+(-n)(-n-1) b x^{-n-2}`
` x^{2} frac{d^{2} y}{d x^{2}}=x^{2}{n(n+1) a x^{n-1}+(-n)(-n-1) b x^{-n-2}}=lambda y`
` lambda y=n(n+1) a x^{n-1+2}+n(n+1) b x^{-n-2+2}`
` lambda y=n(n+1)[a x^{(n+1)}+b x^{(-n)}] `
` lambda y=n(n+1) `
` lambda=n(n+1) `
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