This is a sample problem ffrom my book. They just used the equation for the phenomena of beats, but I was trying to see if I could get the same answer by using the general solution in my first post. I think i know what I did wrong, the sin and cos term in the brackets of the equation I posted...
I found the complimentary solution to be
I think its the particular part of the solution that is confusing me.
The notes say this (its also posted in the 2nd image, but image shack is acting up on display it )
u(t) = u_c(t)+u_p(t)
where
u_c(t) = [A*cos (w_nt)+ B*sin (w_nt)]...
I think maybe I am interpreting the sin(wt) and cos(wt) in the brackets of the general solution wrong. They represent the imaginary and real parts respectively.