" 6.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)+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(1+x^(2)))]^(2) , show that : (1+x^(2))(d^(2)y)/(dx^(2))+x(dy)/(dx)-2=0 .

If y={log(x+sqrt(x^(2)+1))}^(2), show that (1+x^(2))(d^(2)y)/(dx^(2))+x(dy)/(dx)=2

If y={log(x+sqrt(x^(2)+1))}^(2), show that (1+x^(2))(d^(2)y)/(dx^(2))+x(dy)/(dx)=2

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

If y=log (x + sqrt(x^(2) + 1)) then show 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 .

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