Bacteria are supplied as food to a protozoan population at a constant rate . It is observed that the bacteria are consumed at a rate that is proportional to the square of their numbers. The concentration c(t) of the bacteria therefore satisfies the differential equation de = 4- Ac? (2) dt where A is a positive constant. a) Determine the solution behavior in terms of e(0) = co. a) Is there an equilibrium? If so, what is it? Problem 4) Determine the linearly independent solutions for the following: a) 2 1 (3) 3 -2 b) *- () - 3-18 (4) 2 -9