In the paper existence and uniqueness results for the linear differential system on the interval [0,1] $A_1{\left(A_{0}x\right)}^{\text{'}}-A_2^{\text{'}}x=f^{\text{'}}$ with distributional coefficients and solutions from the space of regulated functions are obtained.

The paper deals with the linear differential equation (0.1) ${\left(p{u}^{\text{'}}\right)}^{\text{'}}+q^{\text{'}}u=f^{\text{'}\text{'}}$ with distributional coefficients and solutions from the space of regulated functions. Our aim is to get the basic existence and uniqueness results for the equation (0.1) and to generalize the known results due to F. V. Atkinson [At], J. Ligeza [Li1]-[Li3], R. Pfaff ([Pf1], [Pf2]), A. B. Mingarelli [Mi] as well as the results from the paper [Pe-Tv] concerning the equation (0.1).