I'm currently stuck with a problem where I'm supposed to find all solutions that are asymptotic to the line $y=3-t$ when $t\to \mathrm{\infty}$. This is the demand, from here I'm supposed to create a first order linear differential equation. Can someone help me get started with this problem? Unsure of how to start....

Asymptotic would mean that for example $x(t)=y(t)-1/t$ would satisfy the given demand, not sure how to go further with this although.

A first order linear differential equation means I should have some sort of connection between my function and the derivative of the function, I cant make that connection....

It's my first time using this forum so I've probably made every mistake you can make, hopefully my question is still relevant...