If `y= (cos^-1 x)^2`, prove that: `(1 - x^2 ) ((d^2y)/dx^2) - x(dy/dx) -2 = 0`.

If y= sin (2 sin^-1 x) , prove that: (1 - x^2 ) (d^2y/dx^2) - x(dy/dx) + 4y = 0 .

If y = (sin^-1 x)^2 , then prove that (1 -x)^2 (d^2y)/(dx^2) -x dy/dz =2

Find the second order derivative of the following functions If y = (cos^(-1) x) , then P.T (1 - x^2) (d^2 y)/(dx^2) -x(dy)/(dx) = 0.

If y = cos(2 cos^(-1)x) , then prove that (1 - x^2)(d^2y)/(dx) -xdy/dx + 4y = 0

If y = sin(2 cos^(-1)x) , then prove that (1 - x^2)(d^2y)/(dx) -x dy/dx + 4y = 0

Find the second order derivative of the following functions If y = cos^(-1)x show that (1 - x^2)(d^2y)/(dx^2) - x (dy)/(dx) = 0