Inverse Laplace transformation of (s^2 + s)/(s^2 +1)(s^2 + 2s + 2)

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...

Obtain Laplace transforms for the function ${\displaystyle t^2}$ step(t-2)

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after integrating $\frac{y^{\prime }}{y(x)}=\tan x$
i came up with $\log y(x)=-\log \cos (x)+1.$
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