We take advantage of the complex structure to compute in a short way and without using any computer algebra system the Lyapunov quantities and for a general smooth planar system.
Dettweiler and Reiter formulated Euler's integral transformation for Fuchsian systems of differential equations and applied it to a definition of the middle convolution. In this paper, we formulate Euler's integral transformation for systems of linear differential equations with irregular singularities. We show by an example that the confluence of singularities is compatible with Euler's integral transformation.