- #1

nate9519

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Two very large tanks are each partially filled with 2000 gallons of brine. Initially 5000 ounces of salt is dissolved in tank A and 1000 ounces of salt is dissolved in tank B. The system is closed in that the well stirred liquid is only pumped between the two tanks. Four gallons per minute is pumped from tank A into tank B, while three gallons per minute is pumped from tank B into tank A. This continues until one tank overflows or one tank is empty.

2. Homework Equations

This is the system I have constructed which is consistent with the way my book models this type of problem. If it looks wrong please let me know.

dx/dt = (3y / (2000 - t)) - (4x / (2000 + t))

dy/dt = (4x / (2000 + t)) - (3y / (2000 - t))

3. Attempt at solution

my problem is when I try to solve the system.

(dx/dt) + (4x / (2000 + t)) = (3y / (2000 - t))

4 / (2000 + t) is my integrating factor which turns to (t + 2000)^4 because of the ln. after multiplying through I get

d/dt [ x (t + 2000)^4] = (3y / (2000 - t)) (t + 2000)^4

this is where I am stuck. I have no idea how to integrate the right side. is this the result of a previous error ?