  Given a differential equation on a smooth $p$-adic analytic curve, one may
construct a new one by pushing forward by an \'etale morphism. The main result
of the paper provides an explicit formula that relates the radii of convergence
of the solutions of the two differential equations using invariants coming from
the topological behavior of the morphism. We recover as particular cases the
known formulas for Frobenius morphisms and tame morphisms.
  As an application, we show that the radii of convergence of the pushforward
of the trivial differential equation at a point coincide with the upper
ramification jumps of the extension of the residue field of the point given by
the morphism. We also derive a general formula computing the Laplacian of the
height of the Newton polygon of a $p$-adic differential equation.
