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SC-96-14
In General Relativity, the motion of expanding shearfree perfect fluids is governed by the ordinary differential equation $y^{\prime \prime }=$ $% F(x)\,y^2$ , where $F$ is an arbitrary function from which the equation of state can be computed. A complete symmetry analysis of this differential equation is given; its solutions are classified according to this scheme, and in particular the relation to Wyman's Painlev\'e analysis is clarified.