1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    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.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted