ON A FIRST ORDER LINEAR SINGULAR DIFFERENTIAL EQUATION IN THE SPACE OF GENERALIZED FUNCTIONS($ B)

We investigate the question of the appearance of other kind of solutions of an homogeneous singular linear first -order differential equation not found in the space K’ but existing in the space of rapidly decreasing generalized functions ($ B). Previously in our work, we have already obtained all distributional solutions of the considered equation in the space K’. We want to show in the present investigation the possibility of appearance of other kind of solutions in the space ($ B). For this goal, we use the well known theorems and lemmas from the general theory of generalized functions and theory of linear differential equations. We look for the particular solution in a special chosen way and we formulate step by step the corresponding theorems related to each case for the description of the not zero-centered general solution.