Question

Using operator method solve (general solution):
x'+2y'=4x+5y
2x'-y'=3x
x(0)=1
y(0)=-1

I did:
Dx+2Dy=4x+5y
2Dx-Dy=3x

Then:
(D-4)x+(2d-5)y=0
(2D-3)x-Dy=0

I know how to solve the ones where you're left with just x or just y when you multiply top and bottom by something but not this one.