1. The problem asks to analyze the conditions when $x,y$ are positive and when $x,y$ are real integers. 2. For the case when $x,y$ are positive, we consider $x>0$ and $y>0$. 3. For the case when $x,y$ are real integers, $x,y \in \mathbb{Z}$ (the set of all integers). 4. Without a specific equation or inequality, we cannot solve further, but these are the domain conditions for $x,y$. 5. If you provide an equation or expression involving $x,y$, I can analyze or solve it under these conditions.