Question

Solve the given differential equation: y''-7y'-8y=2e^-x

Answer 1

There are a couple of ways to solve this. One is with the method of undetermined coefficients:
http://wdjoyner.com/teach/DiffyQ/de-undetermined-coeffs.pdf

which is ok.

But the more sophisticated method is to understand more of what's going on here:
http://ocw.mit.edu/courses/mathematics/18-03-differential-equations-spring-2010/video-lectures/lecture-13-finding-particular-sto-inhomogeneous-odes/
(and maybe other lectures before this as well.)

Answer 2

In any case, there are two parts to solving this equation. The first is the find the homogeneous solutions and then the second is to find the particular solution.

I'm guessing (hop

Answer 3

I'm guessing you know how to find the homogeneous solutions. I.e., the solutions to:
y''-7y'-8y = 0