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

Question

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

Answer 1

∵  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