`x(d^2y)/(dx^2)+(dy)/(dx)+x=0`

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

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

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

If y=acos(logx)+bsin(logx), prove that x^2(d^2y)/(dx^2)+\ x(dy)/(dx)+y=0

Verify that y=log(x+sqrt(x^2+a^2))^2 satisfies the differential equation (a^2+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

Find the second order derivative of the following functions If y = (cos^(-1) x) , then P.T (1 - x^2) (d^2 y)/(dx^2) -x(dy)/(dx) = 0.

If y=log\ [x+sqrt(x^2+1)] , prove that (x^2+1)(d^2\ y)/(dx^2)+x(dy)/(dx)=0

If y=log\ [x+sqrt(x^2+1)] , prove that (x^2+1)(d^2\ y)/(dx^2)+x(dy)/(dx)=0

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