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System of Coulped ODE's/ Panic Attack

  1. Mar 29, 2007 #1
    1. The problem statement, all variables and given/known data

    dx/dt = -xy

    dy/dt =-xy

    find x(t) and y(t)


    3. The attempt at a solution

    Using Maple I've plotted the vector field and solution curve for a list of initial conditions. When I tried to work by hand I could find a way to uncoulple the equations. Is there an analytical solution? Method (linearization and etc. )works best? I've sifted through numerous textbooks and couldn't find a decent example.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Mar 29, 2007 #2

    Dick

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    As a first step I would integrate dx/dt=dy/dt.
     
  4. Mar 29, 2007 #3
    Are you telling me its that simple?

    Could you go a little further?
     
    Last edited: Mar 29, 2007
  5. Mar 29, 2007 #4
    1st solve dy/dt = dx/dt. You should then be able to solve for y. Next you could plug y into dx/dt = -xy to get a seperable equation. Then solve for x & y. Be careful with your constants!
     
  6. Mar 30, 2007 #5

    HallsofIvy

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    My first thought was that dy/dx= -xy/-xy= 1 but that is precisely what Dick and pki15 are saying.
     
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