The generalized linear differential equation $dx=d\left[a\right(t\left)\right]x+df$ where $A,f\in B{V}_n^{loc}\left(J\right)$ and the matrices $I-{\Delta }^{-}A\left(t\right),I+{\Delta }^{+}A\left(t\right)$ are regular, can be transformed $\frac{dy}{ds}=B\left(s\right)y+g\left(s\right)$ using the notion of a logarithimc prolongation along an increasing function. This method enables to derive various results about generalized LDE from the well-known properties of ordinary LDE. As an example, the variational stability of the generalized LDE is investigated.

The canonical form theorem, applied to a certain group of symmetry transformations of certain Fuchsian equations, leads automatically to the integration of them. The result can be extended to any n-order differential equation possesing a certain pointlike group of symmetries with a maximal abelian Lie-subgroup of order c.