A classical and a relativistic law of motion for spherical supernovae
  In this paper we derive some first order differential equations which model
the classical and the relativistic thin layer approximations. The circumstellar
medium is assumed to follow a density profile of Plummer type, or of
Lane--Emden ($n=5$) type, or a power law. The first order differential
equations are solved analytically, or numerically, or by a series expansion, or
by recursion. The initial conditions are chosen in order to model the temporal
evolution of SN 1993J over ten years and a smaller chi-squared is obtained for
the Plummer case with eta=6. The stellar mass ejected by the SN progenitor
prior to the explosion, expressed in solar mass, is identified with the total
mass associated with the selected density profile and varies from $0.217 $ to
$0.402 $ when the central number density is $10^7 $ particles per cubic
centimeter. The Full width at half maximum of the three density profiles, which
can be identified with the size of the Pre-SN 1993J envelope, varies from
0.0071 pc to 0.0092 pc.
