Deriving second-order equation

[promach]

What approach should I use to derive the following second order equation (3) ?
Small-signal model does not make sense here, I suppose for derivation ?

 

[CataM]

Use the voltage divider formula in the Laplace domain ("s" domain).

Another way is to use the well known impedances as we learned in high school and then make s=jω

 

[FvM]

I don't understand your question in relation to the quoted text. It's describing a linear second order system, which is obviously a small signal description.

The assumed negative DC/DC input impedance RN is of course only valid for specific load, the converter input impedance is a simplified linear model. RN could be the worst case (minmal) value.