If y= sin-1x/(1-x2)1/2 show that (1-x2)d2y/dx2 - 3x dy /dx -y =0

y=sin-1x1-x2y1-x2=sin-1xDifferentiating both side w.r.t. x, we have,ddxy1-x2=ddxsin-1x1-x2dydx+yddx1-x2=11-x21-x2dydx+y-2x21-x2=11-x21-x21-x2dydx-xy1-x2=11-x2dydx-xy=1Differentiating again both side w.r.t. x, we have,ddx1-x2dydx-xy=ddx11-x2d2ydx2-2xdydx-xdydx-y=01-x2d2ydx2-3xdydx-y=0Hence Proved.

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