If y = cosec^(-1) x,x>1,then show that x(x^2-1)d^2y/dx^2 + (2x^2-1)dy/dx = 0 ​

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If y = cosec-1 x,x>1,then show that x(x2-1)$\frac{d^2y}{dx^2}$ + (2x2-1)$\frac{dy}{dx}=$0

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∵  y = cosec-1x

Differentiating with respect to x, we get

∴ $\frac{dy}{dx}=\frac{-1}{x\sqrt{x^2-1}}$

Again differentiating with respect to x, we get