Solution: 1318 Two-compartment mixing problems are similar to the mixing problems in

Chapter 10, Problem 16

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1318 Two-compartment mixing problems are similar to the mixing problems in Exercises 7.4.4548, except there are two connected tanks of fixed capacities filled with a well-mixed solution of some substance (for example, salt). Solution of a given concentration can enter each tank at a fixed rate, and solution also flows back and forth between the tanks. Solution can also leave each tank at a fixed rate. fc fc d d k k V V Using x1std and x2std to denote the amount of substance in each tank at time t, we obtain the following system of linear differential equations: dx1 dt f1c1 2 k12 x1 V1 1 k21 x2 V2 2 d1 x1 V1 dx2 dt f2c2 2 k21 x2 V2 1 k12 x1 V1 2 d2 x2 V5 Systemic lupus erythematosus In Exercise 10.3.12 wemodeled the amount of antibodies in the bloodstream and inother organs. The system of differential equations describingthe amount of antibody in each compartment isdx1dt G 1 k21 x2 2 k12 x1 2 kx1dx2dt k12 x1 2 k21 x2 where x1 and x2 are the amounts in the blood and organs,respectively (in mg), G is the rate of generation of antibodies,k is the rate at which the drug treatment removes antibodyfrom the bloodstream, and kij is the rate of flow ofantibody from compartment i to j. Explain how these equationscan be viewed as a special case of a general twocompartmentmixing problem.