Applied Differential Equations

Mixing Problems in Differential Equations: Rate In, Rate Out, and Changing Volume

August 30, 2026 Brian M. Woody Leave a comment

Woody Calculus introduction to differential-equation mixing problems, showing a perfectly stirred saltwater tank with inflow and outflow. The governing model is Q′(t) = c_in r_in − [Q(t)/V(t)]r_out. Equal flow rates produce constant volume, while unequal flow rates produce changing volume.

Learn how to model and solve differential-equation mixing problems with rate in minus rate out. Work through constant-volume, draining-tank, and overflow examples, then practice the complete seven-step method.

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