A New Class of Ordinary Differential Equation at Infinity and Its Solution

The main purpose of this paper is to construct a new class of second order differential equation at infinity. To solve the problem, we generate the auxiliary equation via a pre-auxiliary equation and obtain the general solution of it. We express the higher order of the differential equation in a matrix form. We have also studied the problem with a change in variable. We prove the sufficient condition of the solutions for the 2nd order differential equation under certain conditions for existence of the problem.