If `y=log{x+ sqrt( x^2+a^2 )}` , prove that: `(x^2+a^2)(d^2y)/(dx^2)+x(dy)/(dx)=0` .

If y=log{x+sqrt(x^(2)+a^(2))}, prove that: (x^(2)+a^(2))(d^(2)y)/(dx^(2))+x(dy)/(dx)=0

Find the second order derivative of the following functions If y = log[x + sqrt(x^2 + a^2)] , show that (x^2 + a^2) (d^2y)/(dx^2) + x (dy)/(dx) = 0

If y=log[x+sqrt(x^2+a^2)\ ] , show that (x^2+a^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=sin(logx) , prove that x^2(d^2y)/(dx^2)+x(dy)/(dx)+y=0 .

If y= log(x+ sqrt ( x^2 + a^2 ) ), show that ( x^2 + a^2 )( d^2 y)/(d x^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)] , then prove that (x^(2)+1)(d^(2)y)/(dx^(2))+x(dy)/(dx)=0 .