Power Series Solution Of Ordinary Differential Equation And Its Application To Bessel's And Legendre's Equations

                                                           ABSTRACT

Ordinary differential equation as a branch of mathematics is widely applied in the solution of many physical problems; hence the relevance of its study. In this work, we considered the solution of ordinary differential equations of the second order using the power series method, with application to Legendre's and Bessel's equation only. This became necessary as some ordinary differential equations cannot be solved using closed form approach. Summarily, in this work, we considered the basic concepts of power series and ordinary differential equation and also applied it to some ordinary differential problems including Bessel's and Legendre's equation systematically.