  A characterization of the general linear equation in standard form admitting
a maximal symmetry algebra is obtained in terms of a simple set of conditions
relating the coefficients of the equation. As a consequence, it is shown that
in its general form such an equation can be expressed in terms of only two
arbitrary functions, and its connection with the Laguerre-Forsyth form is
clarified. The characterizing conditions are also used to derive an infinite
family of semi-invariants, each corresponding to an arbitrary order of the
linear equation. Finally a simplifying ansatz is established, which allows an
easier determination of the infinitesimal generators of the induced pseudo
group of equivalence transformations, for all the three most general canonical
forms of the equation.
