" If "y=(x+sqrt(1+x^(2)))^(n)," then "(1+x^(2))(d^(2)y)/(dx^(2))+x(dy)/(dx)" is equal to "

If y=(sin^(-1)x)^(2)+(cos^(-1)x)^(2), then (1-x^(2))(d^(2)y)/(dx^(2))-x(dy)/(dx) is equal to 4(b)3(c)1(d)0

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= sin (mlog (x+ sqrt( 1+x^(2)))),then (1+x^(2) ) (d^(2)y)/(dx^(2))+x(dy)/(dx) =

If y=[x+sqrt(x^(2)-1)]^(15)+[x-sqrt(x^(2)-1)]^(15) then (x^(2)-1)(d^(2)y)/(dx^(2))+x(dy)/(dx) is eqaul to

If y=sin(log_(e)x) , then x^(2)(d^(2)y)/(dx^(2))+x(dy)/(dx) is equal to

If y=sin(log_(e)x) , then x^(2)(d^(2)y)/(dx^(2))+x(dy)/(dx) is equal to

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

If y=cos(log x) , then x^(2)(d^(2)y)/(dx^(2))+x(dy)/(dx)+y is equal to