  To approximately compute the non-relativistic ground state of an electrically
non-neutral star, an exactly solvable model was recently introduced, and partly
solved, by Krivoruchenko, Nadyozhin, and Yudin. The model generalizes the
well-known Lane--Emden equation of a polytropic gas ball of index $n=1$ to a
two-fluid setting. Here its complete solution is presented in terms of simple
elementary functions; it is also generalized to a more-than-two-fluid setting
where it remains exactly solvable. It is shown that, given the number of
nuclei, a maximal negatively and a maximal positively charged solution exists,
plus a continuous family of solutions which interpolates between these
extremes. Numerical comparisons show that this exactly solvable model captures
the qualitative behavior of the more physical model it is supposed to
approximate. Furthermore, it correctly answers the question: how non-neutral
can the star be? The answer is independent of the speed of light $c$ and the
Planck quantum $h$. It supports Penrose's weak cosmic censorship hypothesis, in
the sense that the bounds on the excess charge are compatible with the bound on
the charge of a Reissner--Weyl--Nordstr\"om black hole.
