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

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Question

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.

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