Two problems in the Galois theory of differential fields for the field of formal power series

The direct problem in the Galois theory of differential fields for a homogeneous linear differential equation of the second order over the field $\mathbf C((X))$ is solved, and a classification of $SL(2)$-extensions and a description of the Picard–Vessiot extensions of this field are given.
Bibliography: 5 titles.