Consider the nonlinear differential equation x" = x(x-4) 1. Write this equation as a system of nonlinear first order equations in zand. (1 mark) 2. Find the critical points of this system of first order equations. (1 mark) 3. Linearise the equation at each critical point, (2 marks) 4. classify each critical point (2 marks), 5. and make a rough sketch of solutions near to each critical point in the (x,x) phase plane. (2 marks) 6. Attempt a sketch of solutions in the phase plane and give a qualitative description of any different types of solutions, in terms of how x behaves (2 marks, but tricky!)