Classification of $n-$th order linear ODEs up to projective transformations

Classification of $n-$th $(n\ge 2)$ order linear ODEs is considered. The equation reduced to $\mathit{\text{Laguerre-Forsyth}}$ form by a point transformation then, the other calculations would have done on this form. This method is due to $\mathit{\text{V.A.}}\mathit{\text{Yumaguzhin}}$.