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Phase portrait

  1. Feb 7, 2016 #1
    So I have a diff eq
    dy/dx = ky - w

    where K and W are constant's
    I wanna draw a phase portrait
    so i set ky - w = 0

    and determine the expression equals 0 at y = w/k

    so I wanna study the behavior of the solution greater w/k
    and less than w/k
    so I plug (2w/k) and (-2w/k) and check the sign

    so k(2w/k) - w = w Positive


    k(-2w/k) - w = -3w Negative

    Did I determine this correctly? I feel like I am doing something horribly wrong here
  2. jcsd
  3. Feb 8, 2016 #2


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    Gold Member

    you must specify the sign of the constants ##k,w## before, so you know where put the constant solutions on the phase plane ...
  4. Feb 8, 2016 #3


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    Education Advisor

    Yes, assuming your constants ##k## and ##w## are positive, also see the remark by @Ssnow. Is this a simple model of an exponentially growing population with growth rate ##k## and constant harvesting ##w##?

    Two more remarks:
    1. You have a first order equation, so there isn't really a phase plane or a phase portrait but more a phase line.
    2. You probably already knew this, but you can easily solve the ODE explicitly. However, a graphical analysis like yours also gives all the information.
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