Valery A.Yumaguzhin,

Local classification of linear ordinary differential equations.


It is known that any linear ordinary differential equation of order $n\geq 3$
can be transformed to the Laguerre--Forsyth form 
$$
  y^{(n)}=\sum_{i=3}^na_{n-i}(x)y^{(n-i)}
$$
by a point transformation of variables. 

In this short work, we explain without proofs the 
classification of $n\geq 3$ order linear ordinary differential 
equations of the Laguerre--Forsyth form in a neighborhood of a regular 
point up to a contact transformation.