Most of these exercises are of an advanced nature. However, any of the exercises from Chap...

Most of these exercises are of an advanced nature. However, any of the exercises from Chapter 8 may be done using odesolve, so look there for more elementary exercises.

A salt solution containing 2 pounds of salt per gallon of water enters a tank at a rate of 4 gal/min. Salt solution leaves the tank at a rate of 2 gal/min. Initially, the tank contains 10 gallons of pure water. Find the amount of salt in the tank when the volume of solution in the tank reaches 30 gallons. One way to do this problem is to note that the volume of solution in the tank is given by V = 2t + 10 and the salt content is governed by the differential equation xʹ = 8 − 2x/V, with initial condition x(0) = 0. Set V = 30 in V = 2t + 10 and find the time. Then solve the initial value problem and substitute this time to get the salt content. However, odesolve offers another method. Set up the system

Use a time plot to plot both x and V versus t for the solution with initial conditions x(0) = 0 and V (0) = 10. Examine the plot to determine when V = 30 and note the time when this occurs, then estimate the salt content from the plot at this time.