So I have two equations
$X' = aX + bY$
$Y' = cX + dY$
I want to convert it back to a second order equation with the form
$X'' + \alpha X' + \beta X$ with $\alpha,\beta$ in terms of a,b,c,d.
I have been racking my brain for hours trying to go backwards from a reduction of order, but just can't seem to figure it out. Any help would be much appreciated!