`y=[log(x+sqrt(x^2+1))]^2` then prove that `(x^2+1)y_2+x y_1=2`

Similar Questions

Explore conceptually related problems

If y= (x + sqrt(x^(2) + 1))^(m) then prove that, (x^(2)+1) y_(2) + xy_(1)= m^(2)y

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

If 2x= y^((1)/(m)) + y^(-(1)/(m)) (n ge 1) then prove that, (x^(2)-1) y_(2) + xy_(1) = m^(2)y

If y= sin (pt), x= sin t , then prove that (1- x^(2))y_(2)-xy_(1)+ p^(2)y= 0

If y= log (x + sqrt(x^(2) + a^(2))) then (dy)/(dx) = ………

If y= {x + sqrt(x^(2) + a^(2))}^(n) prove that (dy)/(dx)= (ny)/(sqrt(x^(2) + a^(2))). n gt 1 ne N

y= sqrt((1- sin 2x)/(1+ sin 2x)) then prove that (dy)/(dx) + sec^(2) ((pi)/(4)-x)= 0

If y= sin^(-1)x then prove that (1-x^(2))(d^(2)y)/(dx^(2))-x (dy)/(dx)=0

If y= (tan^(-1) x)^(2) show that (x^(2) + 1)^(2) y_(2) + 2x (x^(2) + 1)y_(1) = 2