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Differential equations (typical c4 test question)

  1. Jun 9, 2008 #1
    1. The problem statement, all variables and given/known data
    Liquid is pouring into a container at a constant rate of 20 cm³/s and is leaking out at a rate proportional to the volume of liquid already in the container

    a) Explain why, at t seconds, the volume, V cm³, of liquid in the conainer satisfies the differential equation:

    [tex] \frac{Dv}{dt} = 20 - kV[/tex]
    where k is a positive constant

    The container is initially empty

    b) By solving the differential equation show that

    [tex]V = A + Be^{-kt}[/tex]

    giving the values of A and B in terms of k

    3. The attempt at a solution

    a) Well the change in volume differs with time. 20 cm³/s is pouring in the the container minus a proportional rate of the volume in the container at the time.

    b) NOT SURE

    err do i have to do some flipping of differentials around?

    Thanks :)
  2. jcsd
  3. Jun 9, 2008 #2


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    b) yes... dv / (20-kV) = dt, then integrate and solve for V(t)
  4. Jun 10, 2008 #3


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    In other words, only separation of variables is needed to solve this DE.
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