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Integrating this

  1. Mar 29, 2005 #1
    I have this population differential equation dP/dt=k1(P)-k2(P) where k1 and k2 are proportionality constants. I need to integrate and analyze where k1>k2, k1=k2, and k1<k2. Trouble is, I don't think I'm integrating this right. I get P=e^(t+C)(k1-k2). I know this should be easy but I don't think it's right. Little help?
  2. jcsd
  3. Mar 29, 2005 #2
    the solution is

    [tex]P(t) = Ae^{(k_1-k_2)t}[/tex]

    for some constant [itex]A[/itex], which might be equivalent to yours, or it might not (I can't tell whether you mean that [itex]k_1-k_2[/itex] is in the exponent or not. If it is, then yours is fine).
    Last edited: Mar 29, 2005
  4. Mar 30, 2005 #3


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    Yes,the jonction between the 2 formulae is made simply

    [tex] P(t)=e^{\left[\left(k_{1}-k_{2}\right)(t+C)\right]}=e^{C\left(k_{1}-k_{2}\right)}e^{\left(k_{1}-k_{2}\right) t} =A e^{\left(k_{1}-k_{2}\right) t} [/tex]

    ,where i defined

    [tex] A=:e^{C\left(k_{1}-k_{2}\right)} [/tex]

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