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

If y = sin^-1 x , show that : (1-x^2) d^2y/dx^2- x 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 = 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 = e^(4xtan^-1x) , then show that : (1 + x^2)^2 d^2y/dx^2 + 2x ( l +x^2 ) dy/dx= 16y .

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

If y = e^(4tan^-1 x) , then show that (1+x^2)^2 (d^2y)/(dx^2) + 2x(1+x^2)dy/dx = 16y

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

IF [y= (tan^-1 x)^2 , show that [(x^2 +1)^2 d^2y/dx^2+2x (x^2 + 1)dy/dx=2]