how can find on the particular solution of the linear DE's

d^3y/dx^3+4d^2y/dx^2+4dy/dx=exp(-2x)

take a look here

http://www.wolframalpha.com/input/?i=y%22%27+%2B+4y%22+%2B+4y%27+%3D+e^%28-2x%29