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) \(\frac{d^2y}{dx^2}+(2x^2-1)\frac{dy}{dx}\) = 0

Answer 1

Formula: –

Given: –

Y = cosec^–1x

We know that

Hence proved.