The Formulas for Solution of One Class of Linear Differential Equations of the Second Order with the Variable Coefficients

Abstract

Exact solutions for linear and nonlinear differential equations play an important role in theoretical and practical research. In particular many works have been devoted to finding a formula for solving second order linear differential equations with variable coefficients. In this paper we obtained the formula for the common solution of the linear differential equation of the second order with the variable coefficients in the more common case. We also obtained the new formula for the solution of the Cauchy problem for the linear differential equation of the second order with the variable coefficients. Examples illustrating the application of the obtained formula for solving second?order linear differential equations are given.