# Transfer function's poles and Auxiliary Equation

## Main Question or Discussion Point

Why does the homogeneous of a second order differential equation/system (i.e. a series RLC circuit) is identical to the transfer function (i.e. H(jw)) denominator in its standard form? Therefore the poles of the transfer function are also the solutions for the auxiliary equation...

I cannot see any link between these two things, but they seem to be interrelated somehow. Is there any proof for this?