A favorite application of first order linear ODE systems is to mixing tank problems involving multiple "mixing tanks" of solute and solvent in solution with time evolving concentration. Eigenvalues of the system give characteristic times for reaching equilibrium and for any oscillations which occur in reaching equilibrium (closed systems). This is also a special case of "compartimental analysis" useful in pharmacokinetics (movement of drugs through the body).

- one mixing tank mixode.pdf, mixingtanksolution.pdf [general solution for all parameter values]
- 3tank.pdf, 3tank.mw closed and open 3 tank systems [general solution for all parameter values]
- Edwards and
Penney, Differential Equations and Linear Algebra, section 7.3:

**compartmental analysis: real eigenvalues:**example 2 (open case+comparison with closed case: real/complex eigenvalues)**,**: example 4 (closed case);(more examples 7.3.35,36)];

complex eigenvalues

do 7.3: 37 [closed 3 tank system with oscillations (explanation, text example4.mw), plug into Eq(22), solve by eigenvector method] (solution on-line: .mw, .pdf);

choose one problem from 7.3: 27-30 (solution on-line: .mw).