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

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

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

If x=tan(1/a log y) , prove that (1+x^2) (d^2y)/(dx^2)+(2x-a) (dy)/(dx)=0

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

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

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

If y= (cos^(-1) x)^2 , prove that (1-x^2) (d^2y)/(dx^2) - x(dy)/(dx) -2 =0 , Hence find y_2 when x=0 .

If y = ( cos^(-1) x)^2 , prove that (1-x^2) (d^2 y)/(dx^2) - x(dy)/(dx) - 2=0 . Hence find y_2 when x=0 .

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