Results 1 to 5 of 5

Math Help - separate the variables....

  1. #1
    Senior Member
    Joined
    Aug 2009
    Posts
    349

    separate the variables....

    dp/dt = P - P^2

    ok i am supposed to separate the variables. im having a rough time with this problem..i know to get the p on one side and the dt on the other, and then i used partial fractions to try to integrate and thats when i had problems..

    ln(p) + ln(1-p) = dt

    i dont know im not even sure if thats right and suppose it is right, then when i raise it to e the p's cancel out?? any help would be appreciated.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,547
    Thanks
    1418
    You need to integrate both sides...

    \displaystyle \frac{dp}{dt} = p - p^2

    \displaystyle \frac{1}{p - p^2}\,\frac{dp}{dt} = 1

    \displaystyle \int{\frac{1}{p - p^2}\,\frac{dp}{dt}\,dt} = \int{1\,dt}

    \displaystyle \int{\frac{1}{p-p^2}\,dp} = t + C_1

    \displaystyle \int{\frac{1}{p(1-p)}\,dp} = t+C_1.


    Now follow your instincts to use partial fractions... You can then simplify using logarithm rules.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member
    Joined
    Aug 2009
    Posts
    349
    ok so the integral (A/P + B/(1-P)) ? right then 1 = A-AP + BP ?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor harish21's Avatar
    Joined
    Feb 2010
    From
    Dirty South
    Posts
    1,036
    Thanks
    10
    Quote Originally Posted by slapmaxwell1 View Post
    ok so the integral (A/P + B/(1-P)) ? right then 1 = A-AP + BP ?
    \dfrac{1}{p(1-p)}=\dfrac{A}{p}+\dfrac{B}{1-p}

    1\;=\;A(1-p)+B(p)

    find A and B and then integrate the right side of the above equation
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Banned
    Joined
    Oct 2009
    Posts
    769
    Quote Originally Posted by slapmaxwell1 View Post
    ok so the integral (A/P + B/(1-P)) ? right then 1 = A-AP + BP ?
    Partial fractions method works, but an easier method to break down the fraction (which I refer to as the A-S method or the addition-subtraction method) is to add and subtract p in the numerator of the fraction.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Integral containing two separate sin functions
    Posted in the Calculus Forum
    Replies: 3
    Last Post: June 24th 2010, 04:54 PM
  2. 2 separate wave equation
    Posted in the Trigonometry Forum
    Replies: 0
    Last Post: May 4th 2009, 12:40 AM
  3. How do I separate this in order to integrate?
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 14th 2009, 07:37 PM
  4. Replies: 13
    Last Post: January 5th 2009, 12:15 PM
  5. Performing four separate line integrals
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 11th 2008, 06:58 AM

Search Tags


/mathhelpforum @mathhelpforum