Question

What is the difference between forcing term and non-forcing term and which one is easier to deal with?

Answer 1

A forcing is a function that appears in the equations and is only a function of one independent variable, and not of any of the other variables. For example in capacitor current response the are two terms

One is natural response and other is forced response.

I think the terminology "forcing" comes from mechanics equations originally. In a mechanical system the input is often an actual force. By analogy, you can consider a voltage input to be like a "force" that drives the system.

Both are easy to deal with it depends on how (by what method) you handle them (solve them).