[SOLVED] non-homogeneous differential eqn. - method of undeterminded coefficients

Here is the equation:

I am supposed to solve this differential equation using 2 different methods. Method 1, I understand fine, but method 2 is what I need help understanding.

METHOD 1: Find complete solution using real trial functions. By using , differentiating it and putting it back into the origional equation I got the answer of which IS correct. I got this method down.

METHOD 2: Here are my given directions for "using a complex valued approach"

a) Solve the equation for a patricular solution , where is a complex constant.

b) Expanding ;

c)Noting that: are solutions to both solutions to and respectively.

d)Now by taking the right combination of to obtain a particular solution to the original differential equation.

Hopefully I made what I need to do in method 2 clear, unfortuneatly, I am not clear on how to do it. If anyone would be willing to run throught the solution procedure using this "complex valued approach" I would be thankful.