System of Coulped ODE's/ Panic Attack

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  • #1
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Homework Statement



dx/dt = -xy

dy/dt =-xy

find x(t) and y(t)


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.

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
Dick
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As a first step I would integrate dx/dt=dy/dt.
 
  • #3
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Are you telling me its that simple?

Could you go a little further?
 
Last edited:
  • #4
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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!
 
  • #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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