Method of constructing general solution of the second order linear ordinary differential equations with variable coefficients

Abstract

In this article new method of constructing general solution of the second order linear ordinary differential equations with variable coefficients is presented. The general solutions of Airy equation, of the second order linear ordinary differential equations with variable coefficients and coefficient ex are constructed by this method. Constructed in explicit form general solutions can be used for solving of the Cauchy problem and of the two point’s boundary value problems for ordinary differential equations with variable coefficients arising in solving various applied problems of science.