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App of differentiation

  1. Aug 15, 2010 #1
    1. The problem statement, all variables and given/known data
    dV/dT = 0.15(300-V)
    V is the volume of water in a container at time T. The rate of water flowing into the container is constant at 45 units^3/s. The rate of water leaking is proportional to the volume of water currently in the container. Find the volume of water in the container when T = 20s. Initial volume of water = 0 units^3.

    2. Relevant equations

    3. The attempt at a solution
    I tried integrating the equation but could not get any further. V is a function of time which means that I have no idea in doing this. Could anyone help me? Thanks.
  2. jcsd
  3. Aug 15, 2010 #2


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    Gold Member

    First of all, what is the proportionality of the water leaking? By your equation, I'm assuming your vessel is losing water with a proportionality constant of 0.15/s?

    This is a simple first order differential equation of the form [tex]y'[t] + ay[t] = b[/tex] where differentiation is with respect to time, t. Do you know how to use integrating factors?
  4. Aug 15, 2010 #3
    Ok. Thanks a lot. I have somewhat an idea of how to solve it.
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