If `y=[sin^-1 x]^2`, then prove that : `(1 -x^2) y_2-xy_1 - 2 = 0`.

If y=[tan^-1 x]^2 , then prove that : (x^2 + 1)^2 y_2+2x(x^2+1) y_1 = 2 .

If y=sin(msin^-1x) , prove that (1-x^2)y_2-xy_1+m^2y=0

y = e^(m sin^(-1)x), prove that (1 - x^2) y_2 - xy_1 = m^2y

If y = sin^-1x , prove that (1-x^2)y_2 - x y_1= 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 = (sin^(-1) x)/(sqrt(1 - x^2)) , prove that (1 - x^2) y_2 - 3xy_1 - y = 0

If y = e^(m sin^-1 x) -1lexle1 , show that : (1- x^2)y_2 - x y_1 - m^2y = 0 .

If y = (cos^-1 x)^2 show that (1-x^2)^2 y_2 -xy_1 = 2

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