Ok, lets say I have a first order circuit with i_s = Acos(wt+phase) (like in the pic). I'm having problem with the private solution, lets say I pick my private solution like this: i_p = Bcos(wt + phase) = Ccos(wt) + Dsin(wt) (right?) After I place this i_p in the equation I come up with this: f[C,D]*cos(wt) + g[C,D]*sin(wt) = Acos(wt+phase) (right?) Can I say f[C,D]*cos(wt) + g[C,D]*sin(wt) = Acos(wt)? I mean, How do I come up with C and D? 10x in advance.