"If no controlling current or voltage associated with the dependent source is of interest, we may simply find the Thévenin equivalent connected to the inductor and capacitor."
This is what's written in Engineering Circuit Analysis- Hyatt, Kimberly.
After doing a question this way, I found it a little strange: We're finding the Thevenin Equivalent which includes an independent voltage(Thevenin) source and a Thevenin Resistance, and the total circuit consists of the capacitor and inductor as well. Since it includes an independent voltage source the total response should be the sum of the natural and the forced response, but we're not including the forced response in it. Why so?