# Simple System of de?

• March 26th 2012, 04:34 PM
HolyRiver
Simple System of de?
$dx/dt = x - 0.001xy$

$dy/dt = -y - 0.001xy$

$x(0) = 2000 , y(0) = 1000$

I have no idea how to solve, any tips appreciated! (Nod)
• March 26th 2012, 04:59 PM
pickslides
Re: Simple System of de?
Have you looked at the problem like this?

$\frac{dy}{dx} = \frac{-y(1-0.001x)}{x(1-0.001y)}$
• March 26th 2012, 05:16 PM
HolyRiver
Re: Simple System of de?
Quote:

Originally Posted by pickslides
Have you looked at the problem like this?

$\frac{dy}{dx} = \frac{-y(1-0.001x)}{x(1-0.001y)}$

=

No I didn't but would I then separate variables and then integrate to get $-ln(y) + 0.001y + C = ln(x) - 0.001x$ ? Is this what I should be doing? Not sure how to apply boundary conditions, shoud c = $ln(2000) + ln(1000) -3$

My aim is to find exact values for x(10) and y(10)