We find a solution of the Einstein-Maxwell system of field equations for a class of accelerating, expanding and shearing spherically symmetric metrics. This solution depends on a particularansatz for the line element. The radial behaviour of the solution is fully specified while the temporal behaviour is given in terms of a quadrature. By setting the charge contribution to zero we regain an (uncharged) perfect fluid solution found previously with the equation of statep = μ + constant, which is a generalisation of a stiff equation of state. Our class of charged shearing solutions is characterised geometrically by a conformal Killing vector.

We use the method of preliminary group classification to analyse a particular form of the nonlinear diffusion equation in which the inhomogeneity is quadratic in $u_x$. The method yields an optimal system of one-dimensional subalgebras. As a result we obtain those explicit forms of the unknown functions 𝑓, 𝑔, ℎ and 𝑝 for which the equation admits additional point symmetries.