/sci/ - Science & Math

So, when I typically find solutions, there are scalar variables, but when I do the problem again (using pic), there are no variables just a very particular solution. What am I doing wrong?

I did it on x'' + 3x' + 2x = e^(-5t).
My intended solution is like: Ae^(-t) + Be^(-2t) + (1/12)e^-5t. The solution looks the same, but there aren't any A and B using pic related.