Generalized solutions of the differential first-order equation with the special rational coefficient

Solutions in the space of generalized functions of a linear first-order differential equation in which the coefficient is the generalized function generated by the rational function $\frac{2x-a}{x^2-ax}$, $a>0$ are considered. Conditions for the existence of a generalized solution to the Cauchy problem are found. It is shown that the generalized solution does not exist for all considered coefficients.