In this paper we discuss the package DESOLV written for the algebraic computing system MAPLE. DESOLV has routines which will systematically obtain with considerably flexibility, all resulting integrability conditions for any system of linear, coupled, partial differential equations. It also contains routines which will automatically generate and attempt to integrate the determining equations for the Lie symmetries of differential equations.
We prove that the vorticity or the expansion vanishes for any shear-free perfect fluid solution of the Einstein field equations where the pressure satisfies a barotropic equation of state and the spatial divergence of the electric part of the Weyl tensor is zero.
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