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Math Help - Differential Equation

  1. #1
    Super Member Deadstar's Avatar
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    Differential Equation

    Just revising for my next year courses and going over last years stuff and need to brush up a bit on what should be a simple problem...

    Q) Find the solutions of the following equations of population biology

    \frac{dN}{dt} = k(M - N), N(0) = N_0

    Where k and M are positive constants.

    This really should be easy but after exams I always get a memory block until the courses restart...

    Where I've got up to...

    \lambda + k = 0, \lambda = -k

    so general solution is (M - N)e^{-kt} or something like that... Then you do something like have a particular solution which is just kM... possibly..?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Deadstar View Post
    Just revising for my next year courses and going over last years stuff and need to brush up a bit on what should be a simple problem...

    Q) Find the solutions of the following equations of population biology

    \frac{dN}{dt} = k(M - N), N(0) = N_0

    Where k and M are positive constants.

    This really should be easy but after exams I always get a memory block until the courses restart...

    Where I've got up to...

    \lambda + k = 0, \lambda = -k

    so general solution is (M - N)e^{-kt} or something like that... Then you do something like have a particular solution which is just kM... possibly..?
    see post #2 (and #8, if you want) here. a similar example is worked out
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