If y = (sin^-1x),(√1-x^2) then show that (1-x^2) d^2y/dx^2-3x(dy/dx)-y =0.

Question

If y = \(\frac{sin^{-1}x}{\sqrt{1-x^2}}\), then show that (1-x²)\(\frac{d^2y}{dx^2}-3x\frac{dy}{dx}-y=0.\)

Answer 1

Given,

y = \(\frac{sin^{-1}x}{\sqrt{1-x^2}}\)

Differentiating with respect to x, we get

Again differentiating with respect to x, we get

Answer 2

y=sin-1x/√(1-x2) Read more on Sarthaks.com - https://www.sarthaks.com/50532/if-y-sin-1x-1-x-2-show-that-1-x-2-d-2y-dx-2-3xdy-dx-y-0