If I was stuck, the first thing I would do is find out what case I am dealing with. I would change all the y’s with r’s. Now it’s in a non – homogeneous solution. Now this tells me I can use case 1. After I get my y1 and y2 I would move on to part 2. I now need to find Yp. I would be using the method I learned in my CET 3526 class. It’s where the exponent is D. Or In my case I used r. So -2 is r. I would replace all the rs with -2. I would divided -24e^-2t by (-2-1)(-2-2). Whatever I get is my Yp. Now I have the particular solution. I can plug everything into y(t)= Yh(t) + Yp(t) to get my general solution. That’s how I would solve this problem.