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Differential Equation

  1. Nov 9, 2009 #1
    1. The problem statement, all variables and given/known data
    dP/dt = 2P(1-P)
    write a explicit expression for the dependent variable


    2. Relevant equations

    Seperable equation

    3. The attempt at a solution
    Is the dependent variable P
    does this mean you should write a function of P in terms of t?

    seperation of variables then integration

    lnP - ln(p-1) = 2t + C
    p/(P-1) = e^2t + e^c

    this is all i can get i cannot get an explicit relationship for the dependent variable which is P
    wolfram gave this

    http://www.wolframalpha.com/input/?i=dx/dt+=+2x*(1-x)"

    i cannot get that no idea totally stuck :(
     
    Last edited by a moderator: Apr 24, 2017
  2. jcsd
  3. Nov 9, 2009 #2

    lanedance

    User Avatar
    Homework Helper

    first it doesn't look like you have taken the exponential of the RHS correctly,

    second when you have, multply both sides by (p-1), group p terms & divide by the coefficient you get, hopefully should get you closer

     
    Last edited by a moderator: Apr 24, 2017
  4. Nov 9, 2009 #3

    Mark44

    Staff: Mentor

    The step missing in the middle is
    ln(P/(P - 1)) = 2t + C

    When you exponentiate (make each side the exponent on e), what you ended up with on the right side is incorrect. e^(2t + C) != e^(2t) + e^C
     
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