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If y = sin-1x, show that (1 - x2)\(\frac{d^2y}{dx^2}-x\frac{dy}{dx}=0.\)

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∵ y = sin-1x

Differentiating with respect to x, we get

⇒ \(\frac{dy}{dx}=\frac{1}{\sqrt{1-x^2}}\)

⇒ \({\sqrt{1-x^2}}\frac{dy}{dx}=1\)

Again differentiating with respect to x, we get

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