Using first order linear differential equations to model real life problems. Natural exponential growth and decay problems generally take the form:
Resulting in the following when solved:
Such problems include fluids mixing in tanks, radioactive half life's, etc.
Mixing problems typically take the following form:
From there they can be solved using separable variables or integrating factor methods. See Video 6 - Mixing Problems and Separable Differential Equations for an example.