  Symbolic computation for systems of differential equations is often
computationally expensive. Many practical differential models have a form of
polynomial or rational ODE system with specified outputs. A basic symbolic
approach to analyze these models is to compute and then symbolically process
the polynomial system obtained by sufficiently many Lie derivatives of the
output functions with respect to the vector field given by the ODE system.
  In this paper, we present a method for speeding up Gr\"obner basis
computation for such a class of polynomial systems by using specific monomial
ordering, including weights for the variables, coming from the structure of the
ODE model. We provide empirical results that show improvement across different
symbolic computing frameworks and apply the method to speed up structural
identifiability analysis of ODE models.
