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Differential Equations

  1. May 25, 2008 #1
    An acid solution flows at a constant rate of 6L/min into a tank which initially holds 200L of a 0.5% acid solution. The solution in the tank is kept well mixed and flows out of the tank at 8L/min. If the solution entering the tank is 20% acid then determine the volume of acid in the tank after t minutes.

    I just want to make sure I have the differential equation right.
    let y(t) be the amount of acid solution in the tank.
    rate in = 0.2 * 6 = 1.2L acid per min
    rate out = y(t)/v(t) * 8, where v(t) = 200 - 2t is the volume of liquid in the tank

    So I got

    [tex]
    \frac{dy}{dt} + \frac{8}{200-2t}y=1.2
    [/tex]

    Can someone please confirm that this is the right equation to be working with?
     
  2. jcsd
  3. May 25, 2008 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Yes, that is correct.
     
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