Linear systems of differential equations

Find the general systems of differential equations. You must use the method that includes matrices, eigen values, and eigen vectors. Carefully identify all the important steps.

y1 = y1 + 4y2 - 2cos t

y2 = y1 + y2 - cos t + sin t

I'm sorry, but I can't figure out how to make this stuff work! I rermember how to do most of the steps, I think, but it isn't working together. This is a practice problem, but my teacher assured me that there will be one just like it on the test on Monday, April 30. Could someone please show me how to do this so that I will know how to work on like it on the test?!?!? Thank you.