mixing tank problems

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 concentrations. 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). The single tank starts the analysis at the beginning of the DE course.