System of Coulped ODE's/ Panic Attack

[H-bar None]

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

[Dick]

As a first step I would integrate dx/dt=dy/dt.

[H-bar None]

Are you telling me its that simple?

Could you go a little further?

[pki15]

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!

[HallsofIvy]

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