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Trying to solve a rather difficult differential equation

  1. Apr 9, 2015 #1
    1. The problem statement, all variables and given/known data
    Consider a system composed of two species X and Y with fractional populations x and y, respectively, where x+y=1. The two species interact in such a way that the differential equation for x is:

    \begin{equation}
    \frac{dx}{dt}=xyA_{0}e^{-\alpha t}
    \end{equation}

    where $A_{0}$ and $\alpha$ are non-negative constants. Solve the equation by separation of variables and hence show that the solution for x(0) = $x_{0}$ is:

    Photo attached- too long to write out!

    2. The attempt at a solution

    Again... attached. The problem that I am having is that I can't make x the subject of the equation because I end up with x/(x-1) on the left hand side.
     

    Attached Files:

    Last edited: Apr 9, 2015
  2. jcsd
  3. Apr 9, 2015 #2
    Are you saying that you don't know how to solve that final algebraic equation for x?
     
  4. Apr 9, 2015 #3

    SammyS

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    Those sideways images are very difficult to read.

    I did use the 'Windows' snipping tool to show the solution you are to verify, then pasted it into a word processor app. & rotated it. Capture4.PNG
    Chet's got the rest.
     
  5. Apr 10, 2015 #4
    Don't worry, I was a little tired last night doing a 5 hour practice paper. I've got it now... silly me.
     
  6. Apr 10, 2015 #5

    SammyS

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    Good.

    To make x the subject either of the following forms might have helped.

    ##\displaystyle\ \frac{x}{x-1}=\frac{1}{1-1/x}=1+\frac{1}{x-1}\ ##
     
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