  We investigate the master nonlinear partial differential equation that
governs the evolution of shear-free spherically symmetric charged fluids. We
use an approach which has not been considered previously for the underlying
equation in shear-free spherically symmetric spacetimes. We derive a fifth
order purely differential equation that must be satisfied for the underlying
equation to admit a Lie point symmetry. We then perform a comprehensive
analysis of this equation utilising the Lie symmetry analysis and direct
integration. This enables us to reduce the fifth order equation to quadratures.
Earlier results are shown to be contained in our general treatment.
