A solutes in bloodstream stream enter cells through a process called osmosis. Let $C=C(t)$ be the concentration inside a particular cell. The rate at which the concentration inside the cell is changing is proportional to the difference in the concentration of the solute in the bloodstream and in the cell. Suppose the concentration in the blood is constant $L $.
Find a differential eqn for $dC/dt$.
Your differential eqn will involve anew undetermined proportionality constant, what is it's sign?
Find all equilibrium solutions and their stability.
Ans:
I have worked out my differential eqn to be $dC/dt=k(L-C)$
I've determined my $k$ (prop const) is positive because if L>C then I expect my DE to be positive, which it is. Am I correct so far?
Also how do I answer the 3rd part?