Application of integral formulas for solving ordinary differential equations of the second order with variable coefficients

The article considers linear ordinary differential equations of the second order with variable coefficients (initial equations). Along with each initial equation the same equation is considered only with constant coefficients (accompanying equation). It is shown that the general solution of the initial equation is represented in the integral form through the general solution of the accompanying equation and the fundamental solution of the original equation. The fundamental solution is the perturbation method in the form of an infinite rows. Research is carried out on the convergence of rows. As a concrete example of the application of the developed methodology is considered the Chebyshev equation.