A.maths differentiation

1. Let y= √(ax+b) , where and b are real constants.
Show that
y(d^2y/dx^2)+(dy/dx)^2 = 0

2. Let x^3 - 3xy = 1.
(a) Show that x(dy/dx) + y - x^2 = 0
(b) Hence, show that x(d^2y/dx^2) + 2 (dy/dx) -2x = 0

3. Let Y = 3/√(1+x^2)
(a) Show that (1+x^2)(dy/dx) + xy = 0
(b) Hence, show that (1+x^2) (d^2y/dx^2)+ 3x(dy/dx) + y =0

4. Let y = (x^2 + 1 )^n , where n is a real constant.
(a) Show that (x^2 + 1)(dy/dx) = 2nxy
(b) Hence , show that (x^2+1) (d^2y/dx^2) - 2(n-1)x(dy/dx) - 2ny=0