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

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

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

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

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

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

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