Modified Integral Homotopy Expansive Method to Find Power Series Solutions of Linear Ordinary Differential Equations about Ordinary Points

This article presents the Modified Integral Homotopy Expansive Method (MIHEM) which is utilized to find power series solutions for linear ordinary differential equations about ordinary points. This method is a modification of the integral homotopy expansive method. The proposal consists in providing a versatile, easy to employ and systematic method. Thus, we will see that MIHEM requires only of elementary integrations and that the initial function will be always the same for the linear ordinary differential equations of the same order which contributes to ease the procedure. Therefore, it is expected that this article contributes to change the idea that an effective method has to be long and difficult, such as it is the case of Power Series Method (PSM). This method expresses a differential equation as an integral equation, and the integrand of the equation in terms of a homotopy. We will see along this work the convenience of this procedure.

Automated summary

This article introduces the Modified Integral Homotopy Expansive Method (MIHEM) for finding power series solutions to linear ordinary differential equations about ordinary points. The method is a modification of the integral homotopy expansive method and provides a versatile, easy to use, and systematic approach. MIHEM requires only elementary integrations and the initial function remains the same for differential equations of the same order, making the procedure more straightforward.