FIRST ORDER DIFFEQS (Cont’d) (Applications)

We are going to consider four real-life (well …) situations and will attempt to use our newly acquired expertise with first order differential equations to obtain satisfactory solutions. Our procedure will consist of three steps: A. Carefully list the “givens” and, if appropriate, what is being asked. B. Set up and solve the appropriate differential equation (the mathematical model.) C. Interpret the solution. We do step A. for each of the four situations first.

First situation:

2nd situation:

3 rd situation:

4 th situation: NASA (Rocket Science) Givens:

If the rate of inflow is different from the rate of outflow, (the tank will eventually overflow of become empty), then the diffeq becomes: