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Logistic growth model, differential equation

  1. Apr 10, 2013 #1
    1. The problem statement, all variables and given/known data
    dY/dt = y(c - yb)

    C and B are constants.
    Im supposed to find and explicit solution for y, but im having trouble.

    2. Relevant equations



    3. The attempt at a solution

    dY/y(c - yb) = dt
    ∫(1/c)dy/y + ∫(b/c)dY/c - yb = ∫dt (i used partial fraction decompositions)
    (1/c)ln|y| - (b/c)ln|c - yb| = t + K (K stands for an arbitrary constant)
    ln|[(c-yb)^b]/y| = -ct + K (Multiplied by negative c and then combine the natural logs on the left)

    What im having trouble with is the last expression on the LHS. I have (c-yb)^b so how am I supposed to solve for y, if i dont know b?
     
  2. jcsd
  3. Apr 10, 2013 #2

    Curious3141

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    Homework Helper

    It's very difficult to read what you wrote (use LaTex!!), but there's an error here:

    (1/c)ln|y| - (b/c)ln|c - yb| = t + K

    That should be: ##\displaystyle \frac{1}{c}\ln|y| - \frac{1}{b}.\frac{b}{c}\ln|c-yb| = t + K## so that coefficient of b should cancel out.
     
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