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Math Help - Gompertz differential equation proof

  1. #1
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    Gompertz differential equation proof

    I have no idea what this question is asking me:

    27. Show that y = Me^{ae^{kt}} is a solution for any constant a.

    it gives me this hint:
    dy/dt = ky ln(y/m).

    I would assume that because it is an exponent that any constant for a would give a definable solution.
    I do not know what it is I am trying to prove or what is going on, any help would be appreciated.

    Thanks.
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  2. #2
    MHF Contributor
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    I think that this problem is given in a context that deals with the Gompertz differential equation. You have not provided this equation, so it is not clear a solution to what is being discussed.
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  3. #3
    A Plied Mathematician
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    With your function

    y=Me^{ae^{kt}}, its derivative is

    y'=Me^{ae^{kt}}(ae^{kt})k.

    Also note that

    ky\ln(y/M)=kMe^{ae^{kt}}\ln(e^{ae^{kt}})=kMe^{ae^{kt}}(ae^  {kt}).

    Does that look familiar?
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