Equivalence groupoids of classes of linear ordinary differential equations and their group classification

Admissible point transformations of classes of $r$th order linear ordinary differential equations (in particular, the whole class of such equations and its subclasses of equations in the rational form, the Laguerre-Forsyth form, the first and second Arnold forms) are exhaustively described. Using these results, the group classification of such equations is revisited within the algebraic approach in three different ways.

Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients

Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients are exhaustively described over both the complex and real fields. The exact lower and upper bounds for the dimensions of the maximal Lie invariance algebras possessed by such systems are obtained using an effective algebraic approach.