If `y = sin^-1 x`, show that : `(1-x^2) d^2y/dx^2- x dy/dx=0`

If y = tan^-1 x , show that : (1+x^2) d^2y/dx^2+ 2x dy/dx=0

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

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

If y = e^(2tan^-1x) , then show that : (1 + x^2)^2 d^2y/dx^2 + 2x ( l +x^2 ) dy/dx= 4y .

If y = e^(3tan^-1x) , then show that : (1 + x^2)^2 d^2y/dx^2 + 2x ( l +x^2 ) dy/dx= 9y .

IF [y= (sin^-1) /sqrt(1-x^2)] show that : [(1 -x^2) (d^2y /dx^2) - 3x(dy/dx) -y =0]

If y = e^(acos^-1x), -1lexle1 , show that (1-x^2)(d^2y)/dx^2 - x(dy/dx) - a^2y = 0