$\displaystyle dx/dt = x - 0.001xy$

$\displaystyle dy/dt = -y - 0.001xy$

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

I have no idea how to solve, any tips appreciated! (Nod)

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- Mar 26th 2012, 04:34 PMHolyRiverSimple System of de?
$\displaystyle dx/dt = x - 0.001xy$

$\displaystyle dy/dt = -y - 0.001xy$

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

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

$\displaystyle \frac{dy}{dx} = \frac{-y(1-0.001x)}{x(1-0.001y)}$ - Mar 26th 2012, 05:16 PMHolyRiverRe: Simple System of de?
=

No I didn't but would I then separate variables and then integrate to get $\displaystyle -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 = $\displaystyle ln(2000) + ln(1000) -3 $

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