y sqrt(n^(2)+1)=log(sqrt(n^(2)+1)-n)quad " show "quad " hal "-(n^(2)+1)(dy)/(dx)+my+1=0

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

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

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

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

IF y=A (x+sqrt(x^2-1))^n+B(x-sqrt(x^2-1))^n , Show that, (1-x^2)(d^2y)/(dx^2)-xdy/dx+n^2y=0

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

If the major axis is n times the minor axis of the ellipse,then eccentricity is 1) (sqrt(n-1))/(n) 2) (sqrt(n-1))/(n^(2)) 3) (sqrt(n^(2)-1))/(n^(2)) 4) (sqrt(n^(2)-1))/(n)