Solve part d only

This is yet another variation on the chemostat. Suppose that there is a membrane that filters the outflow, so that the microorganism never flows out (only the nutrient does). Assume, however, that the microorganism dies at a certain rate N. (a) Write down a model, assuming r(C) is Michaelis-Menten. (b) Find a change of variables that leads to a system with three parameters as follows: dtdN=1(C+1C)N3NdtdC=(C+1C)NC+2 (c) Show that there are two steady states, the first one with N=0 and the second one with N=0. Show that this second equilibrium has positive coordinates provided that: 1>3&2133>0, (d) Show that this second equilibrium is always stable (if it has positive coordinates)