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Math Help - Differential problem

  1. #1
    Junior Member
    Joined
    May 2009
    Posts
    27

    Differential problem

    I'm stuck >.<

    Also can someone refer me to some good online material with similar problems to this.

    A person is trying to fill her new swimming pool for the first time. Water is
    flowing into the pool at a constant rate of 30 litres/min. Unfortunately there is a hole and a crack in the pool from which water is leaking. Water is leaking out of the hole at a rate proportional to the square of the amount of water currently in the pool while water is leaking out of the crack at a rate proportional to the amount of water currently in the pool. As it had rained the previous day, the pool already contained 20 litres of water before filling began. Let t (mins.) be the time since the person started filling the pool and let W(t) be the number of litres of water in the pool at time t. Find, but do not solve, the differential equation for W(t) along with its initial condition.
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  2. #2
    Member
    Joined
    Oct 2009
    Posts
    82
    dW/dt = inflow - outflow

    inflow = 30 litres/min
    outflow = k*W^2 + p*W where k,p are constants

    The rest is history. Can you find the initial condition yourself?
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