Aim

The aim of this experiment is to solve first-order Ordinary Differential Equations (ODEs) using the power series expansion technique by carrying out the following steps:

1. To represent the unknown function as a Taylor or power series around a chosen initial point.
2. To substitute the series expansion into the given differential equation.
3. To determine the coefficients of the series using the initial condition and the differential relationship.
4. To generate an approximate analytical solution in power series form.
5. To evaluate and visualize the behavior of the solution within a specified domain.
6. To understand the effectiveness of power series methods for solving ODEs where standard analytical techniques are complex or inapplicable.