differential equations problem: We have two tanks, each containing 360 liters of salt solution. Pure water pours into tank A at a rate of 5 L/min. There are two pipes connecting tank A to tank B. The first pumps salt solution from tank B into tank A at a rate of 4 L/min, and the second pipe pumps salt solution from tank A into tank B at a rate of 9 L/min. Finally, there is a drain on tank B from which salt solution leaves tank B at a rate of 5 L/min. Thus, each tank maintains a constant volume of 360 liters of salt solution. Initially, there are 60 kg of salt presented in tank A, but tank B contains 0 kg of salt. Part 1) Set up, in matrix-vector form, an initial value problem that models the salt content in each tank over time. Part 2) Find the general solution to the system you set up in part (1), which satisfies the initial conditions
differential equations problem:
We have two tanks, each containing 360 liters of salt solution. Pure water pours into tank A at a rate of 5 L/min. There are two pipes connecting tank A to tank B. The first pumps salt solution from tank B into tank A at a rate of 4 L/min, and the second pipe pumps salt solution from tank A into tank B at a rate of 9 L/min. Finally, there is a drain on tank B from which salt solution leaves tank B at a rate of 5 L/min. Thus, each tank maintains a constant volume of 360 liters of salt solution. Initially, there are 60 kg of salt presented in tank A, but tank B contains 0 kg of salt.
Part 1) Set up, in matrix-vector form, an initial value problem that models the salt content in each tank over time.
Part 2) Find the general solution to the system you set up in part (1), which satisfies the initial conditions.
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 3 images