# Solving a system of linear ODEs

Based on my previous post, I have been stuck on this for a few hours now. I want to solve for $x$ and $y$ from the equation $$\frac{dx}{dt} + \frac{dy}{dt}=a-(b+c+d)y-bx.$$

The original two equations are: $$\frac{dx}{dt}=a-bx-\frac{cxy}{x+y} \\ \frac{dy}{dt}=\frac{cxy}{x+y}-(b+c+d)y$$

$a,b,c,d,x,y$ are all nonnegative.

What is the best strategy?

-
IF you have two variables, shouldn't you have 2 equations? – PA6OTA Jun 15 '14 at 18:30
I combined two equations into one by canceling out a nonlinear term. Is two equations mandatory? – Anonymous Jun 15 '14 at 18:35
@Anonymous probably you should show us the problem in its primordial form. – James S. Cook Jun 15 '14 at 19:24
@James S. Cook OK. Anything to get some help! See edit. – Anonymous Jun 15 '14 at 19:31
@Amzoti Hi Amzoti! Simply that they are all nonnegative. – Anonymous Jun 15 '14 at 20:33