I am studying the predator prey equation recently, and here is an example:
Let $x'=x(1-0.5y)$ and $y'=y(-0.75+0.25x)$. This is a predator prey equations. Then $$\frac{dy}{dx}=\frac{y'}{x'}=\frac{y(-0.75+0.25x)}{x(1-0.5y)}$$
This is an exact equation and can be easily solved. It follows that $$0.75\ln x+\ln y-0.5y-0.25x=c$$
where $c$ is a constant.
Then my book says 'it can be shown that this is a closed curve'. I don't think it is obvious and can anybody tell me why it is closed?