Notes on the zeros of the solutions of the non-homogeneous Airys equation

We present some observations on the distribution of the zeros of solutions of the nonhomogeneous Airys equation. We show the existence of a principal family of solutions, with simple zeros, and particular solutions, characterized by a double zero in a given position of the complex plane. A recursion, describing the distribution of the zeros, is introduced and the limits of its applicability are discussed. The results can be considered a generalization of previous works on the distribution of the zeros for the solutions of the corresponding homogeneous equation