y=(x+sqrt(x^(2)-1))^(n)quad PTquad (x^(2)-1)((dy)/(dx))^(2)=m^(2)y^(2)

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

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

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

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