# If y = sin^(-1)x, show that (1 - x^2) d^2y/dx^2-x(dy/dx)=0. ​

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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