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Math Help - Differential Eq. Mixing Problem

  1. #1
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    Differential Eq. Mixing Problem

    The question is a typical mixing problem from differential equations, and the issue with my answer is in lines 12-13, probably has something to do with my integration of the right hand side. I've been at that for hours and I swear I'm doing it properly. Any hints you have would be wonderful
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  2. #2
    Forum Admin topsquark's Avatar
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    Line 14 has an inconsistency with the initial data. The equation on 13 gives A as a function of time, so A(0) = 40. But when we set t = 0 in that equation and solve for A(0) we get A(0) = 0.0002, not 40. Otherwise your derivation and work look correct, so the only interpretation I can come up with is that your initial data is flawed.

    -Dan
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  3. #3
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    Thanks topsquark, you pointing out line 14 was very helpful I didn't think to check it against the given data. To rephrase what you said to me: using algebraic simplification we should be able to see that A(0) = Anot where instead it actually turns out to be something like A(0) = -2*100 + Anot

    I can see that there is an issue in there, the actual problem out of the book is as follows:

    A tank initally contains 100 gal of a solution that holds 40lbs of chemical. A solution containing 2lb/gal of the chemical runs into the tank at the rate of 2 gal/min and the mixture runs out at the rate of 3 gal/min. How much chemical is in the tank after 50 mins?

    Looking back through the data the initial volume = Vnot = 100
    inital amount of chemical = Anot = 40
    concentration in = cin = 2
    rate in = rin = 2
    rate out = rout = 3
    All of which is the proper datums from the problem. Which leaves me thinking that given my calculus is correct I must have totally misunderstood the problem and royally mucked it up in the setup phase, can anyone confirm/deny this?

    And lastly what is the math markup language used here so I can stop looking like a fool when I post :-)

    Thanks in advance
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