I am trying to look whether there exist solutions to a system of 3 differential equations. The differential equations are given by
$$ x' = \dfrac{a}{(1-z)y}$$ $$ y' = \dfrac{b}{(1-x)z}$$ $$ z' = \dfrac{c}{(1-y)x}$$
where all variables are functions of k, derivatives are derivatives with respect to k. a,b, and c are known functions of k.
I actually have never seen a system of differential equations that look like this. Any thoughts on methods how to check whether there exist solutions given initial values?