Valery A.Yumaguzhin,

Classification of linear ordinary differential equations. I.

It is well-known that dimension of algebra of point symmetries of 
an arbitrary $n\geq 3$ order linear ordinary differential equations
can be equal to one of the numbers $n+4$, $n+2$, or $n+1$.

It is well-known that any linear ordinary differential equation 
can be transformed to the form 
$$
  y^{(n)}=\sum_{i=2}^na_{n-i}(x)y^{(n-i)}
$$
by a point transformation of variables. 

In this work, we give the classification of $n\geq 3$ order linear 
ordinary differential equations of this form with $n+4$ and $n+2$ 
dimensional algebras of point symmetries in a neighborhood of a 
regular point up to a contact transformation.