ON CLASSICAL SOLUTIONS OF A SINGULAR LINEAR DIFFERENTIAL EQUATION OF 2ND-ORDER IN THE SPACE K’.

The main goal of this work is to describe all classical solutions of the homogeneous second order linear singular differential Euler equation in the space of generalized functions K'. We focus our investigations only to the situation called Euler case when it is realized respectively the condition m =r+2,n=r+1. For this aim, we look for the regular classical solutions by replacing the general form of the particular solution with the unknown λ, defined by y(x)=x^λ, into the investigated equation. Depending of the nature of the unknown λ we write the corresponding classical solution in the space K'. In this same work, we also use our previous results obtained in the case of the non homogeneous equation with Dirac delta function or it derivatives of s-order to write the general solution of the considered equation with dependence of various cases studied related to the relationships between the parameters.