  It is well known that confinings and asymptotic freedom are properties of
quantum chromo-dynamics (QCD). But hints of these features can also be observed
at purely classic levels. For this purpose we need to find solutions to the
colorly-sourceful Yang-Mills equations with both confining and asymptotic
freedom features. We provide such a solution in this paper which at the
near-source region is of serial form, while at the far-away region is
approximately expressed through simple elementary functions. From the solution,
we derive out a classically non-perturbative beta function describing the
running of effective coupling constant, which is linear in the couplings both
in the infrared and ultraviolet region.
