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Separation of variables D.E.

  1. Apr 26, 2012 #1
    1. The problem statement, all variables and given/known data
    dP/dt=P-P^2


    2. Relevant equations



    3. The attempt at a solution

    I know you can separate this and after i did that and did my partial fractions i got

    t + C = ln(P) + ln(1-P) but i dont know what to do from here i figure you take the e of both sides at some point but i never ended up with the right andswer please help
     
  2. jcsd
  3. Apr 26, 2012 #2

    LCKurtz

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    I think you have a sign error in your solution. You need to fix that and remember the formulas like ln(a)+ln(b) = ln(ab) and ln(a) - ln(b) = ln (a/b).
     
  4. Apr 27, 2012 #3
    i'm not seeing where the sign error is coming from...for my partial fractions i did

    A/P + B/(1-P), then getting rid of the denominators i get A(1-P) + Bp = 1

    solving for A and B i get A=1, B=1

    so wouldn't it be ln(P) + ln(1-P)??

    the only thing i could think is that it should be A(1-P) - BP

    but i don't really understand how it could come out as a subtraction
     
  5. Apr 27, 2012 #4
    Your partial fraction should be 1/P - 1/(P-1).
     
  6. Apr 27, 2012 #5

    LCKurtz

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    Your sign is wrong on your integration of$$
    \int\frac 1 {1-P}\, dP$$
     
  7. Apr 27, 2012 #6
    I see i was messing up my U-substitution, it's always the little things lol thanks for the help
     
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