Differential Equations - Series Solutions
Overview
The series solution method postulates a solution of the form
{% y(x) = x^s \sum_{i=0}^\infty a_i x^i %}
where {% s %} is chosen such that {% a_0 %} is non-zero.
The solution is plugged back to the equation it is meant to solve. This will generate a set of equations that will
specify what the values of {% s %} and each {% a_i %} are. Typically this occurs through the use of a
recurrence relation which specifies how to calulate the values of later values of {% a_i %} from earlier values.
Examples
The following are simple examples that demonstrate the method.
Topics
The following are famous series solutions to specific differential equations encountered in applied math.
