How to approach differential equations with separate x and y?

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I am studying population modelling, and most of the studies I looked at was in this format, which I was not familiar with.

Previously I was looking at basics such as logistic models, delayed logistic models, models with predation. In these, I was mostly dealing with N’(t) functions, and never x and y separately.

Sorry for a basic question, but answers or redirection to other sources would be appreciated.

figure 1.1 is confusing