Hi there!

All you do is just algebra

Consider the following system of 2 equations (linear, inhomogeneous DEs)

where and

rewrite the system using differentials:

Now, let's divide the second equation by the first, in order to eliminate the independent variable t:

or

Now, we have a new, 1st order DE, where is the dependent and 'x' is the independent variable

***

But I suspect you meant something different:

Let's take our system again:

Now, we take the first equation and:

(1). Differentiate it with respect to 't':

(2). Express y with x:

What we do now is gradually plug the second equation of the system into (1) and then plug (2) in the resulting equation:

and

let's rearrange a bit:

this should be the general case of inhomogeneous 2nd order system. You can try it with the 4rth order system