Consider an ODE has the form
The solution can be represented in the form
Regular point and singular point
Rearrange the equation above
Insert this into (*)
(**) is called Indicial equation.
There should be 3 cases of roots.
Frobenius theorem: Let
Case 1: Distinct roots, not differed by integer (e.g. 0, 1/3). General solution is given by
Case 2: Double root (e.g. 1/2, 1/2). General solution is given by
Case 3: Distinct root, differed by integer (e.g. 0, 1,
). General solution is given by
Last Updated on 2 years by Yichen Liu