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Solving Inseparable Differential Equations

Consider the following very simple model of blood cholesterol levels based on the fact that cholesterol is manufactured by the body for use in the construction of cell walls and is absorbed from foods containing cholesterol: Let C(t) be the amount (in milligrams per deciliter) of cholesterol in the blood of a particular person at time t (in days). Then

dC = k1 (C0 - C) + k2E,

C0 = the person's natural cholesterol level,
k1 = production parameter,
E = daily rate at which cholesterol is eaten, and
k2 = absorption parameter

How can I solve this differential equation? It seems as though it is not separable, so I am unsure. I know I want to get C on one side and t on the other, but how do I do this properly since it's not separable (or at least I don't think it is)?

See attached file for full problem description.


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An inseparable differential equation is solved. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.