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!

Homework Help: Separation of variables D.E.

  1. Apr 26, 2012 #1
    1. The problem statement, all variables and given/known data

    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


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    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


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook