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It is known that charged relativistic shear-free fluid spheres are described by the equation y xx = f (x)y 2 + g(x)y 3 , where f and g are arbitrary functions of x only and y is a function of x and an external parameter t. Necessary and sufficient conditions on f and g are obtained such that this equation possesses the Painlevé property. In this case the general solution y is given in terms of solutions of the first or second Painlevé equation (or their autonomous versions) and solutions ofdoi:10.1088/0264-9381/18/1/302 fatcat:5wm7xoymv5gqlfke2mbitkecwi