Is there a way to solve for example:
Where $D$ is the differential operator.
$$(D-4)x + D^2y = 0$$
$$(D+1)x + Dy = 0$$
Without the operator
$$x' - 4x + y'' = 0$$ $$x' + 1x + y' = 0$$
Using a matrix and then row reducing into echelon form?
I'm not sure how to set this up and solve it, to get the coefficients of the form $AD^2+BD+C$.
$(0D^2+1D-4)x + (D^2+0D+0)y = 0$
$(0D^2+1D+1)x + (0D^2+1D+0)y = 0$
I know this is a complex problem and appreciate any help!