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.