Understanding a Homework Statement | Explanation and Solution Tips

[-EquinoX-]

Homework Statement

I have my notes below, however I don't understand the part where it says that:

xp(t) = A, where did this come from?

http://img142.imageshack.us/img142/4733/questionub.th.jpg

Homework Equations

The Attempt at a Solution

 

[tiny-tim]

Hi -EquinoX-!

You have x'' -6x' + 5x = 5.

The general solution is the characteristic solution plus any particular solution.

For the particular solution, you make an intelligent guess …

in this case, it seems obvious that a constant will do (in fact, I don't know why he bothered to say let x_p(t) = A, and solve for A … I'd just have gone straight to x_p(t) = 1)

(but if there was a 5x on the RHS, you'd choose a linear function, if there was an e^7x, a multiple of e^7x, and so on)