Contact Classification of Linear Ordinary Differential Equations: I

It is known that a linear ordinary differential equation of order n3 can be transformed to the Laguerre–Forsyth form y⁽ⁿ⁾=_i=3ⁿa_n–i(x)y^(n–i) by a point transformation of variables. The classification of equations of this form in a neighborhood of a regular point up to a contact transformation is given.