  We study the radius of convergence of a differential equation on a smooth
Berkovich curve over a non-archimedean complete valued field of characteristic
0. Several properties of this function are known: F. Baldassarri proved that it
is continuous and the authors showed that it factorizes by the retraction
through a locally finite graph. Here, assuming that the curve has no boundary
or that the differential equation is overconvergent, we provide a shorter proof
of both results by using potential theory on Berkovich curves.
