I am trying to solve the system of differential equations
dx/dt = (y-x)/(x+y), dy/dt = -y/(x+y), where x and y are functions of t, and x(0)=0, y(0)=c (positive constant). I would like to find x and y explicitly in terms of t. 


This problem is related to my previous question "Probability problem with solution involving e."


Any help would be appreciated. Thanks. 



System of ordinary differential equations
Continuing Michael's answer: Solve $dy/dx = y/(x-y), y(0)=c$ to get (in terms of the Lambert W function) $y(x) = \operatorname{e} ^{W(-x/c) + \mathrm{log} (c)}$. Substitute this into the original equations to get a single equation:
$$
\frac{d x (t)}{d t} = \frac{\operatorname{e} ^{\Bigl(W \Bigl(-\frac{x (t)}{c}\Bigr) + \operatorname{log} (c)\Bigr)} - x (t)}{\operatorname{e} ^{\Bigl(W \Bigl(-\frac{x (t)}{c}\Bigr) + \operatorname{ln} (c)\Bigr)} + x (t)}
$$
$x(0)=0$. Maple finds two solutions for this 


**added** 


The one that seems to work for real $c > 0$ is:
$$x(t) =
-\left(W\_{-1} \left(\frac{-(-t + 2 c) \operatorname{e} ^{-2}}{c}\right) + 2\right) \operatorname{e} ^{\Biggl(tW\_{-1} \Biggl(\frac{-(-t + 2 c) \operatorname{e} ^{-2}}{c}\Biggr) + 2\Biggr)} c
$$


