I am WEAK in DE's. I have been trying to understand this question all day. I posted the question as an image since I don't have enough rep points to post it here.
http://images.4chan.org/sci/src/1327448267650.jpg
There is one example in my text Butkov on how to do this but it is not clear at all to me what I must do!
so far I just wrote:
L* i"(t) + R* i'(t) + (1/C) i(t) = -Vo*ω*sin(ω*t)
I then took a function f(t) = F*exp(i*t)
where F = Vo*ω, and so F*exp(i*t) = Vo*ω(cosωt - i*sinωt)
I then wrote im{Vo*ω*exp(-it)} = -Voωsinωt
I clearly have no idea what I am doing. Please, any help would be appreciated.