While studying recurrence relation I figured out that to find General solutions we have different formula's for different scenarios.
For eg, say we have 2 characteristic roots for a Homogeneous formula, then we use a specific formula, say A1*α1^n + A2*α2^n. Here, α1 and α2 are the two char roots. Similarly, we will add A3*α3^n and so on as the number of char roots increases.
However, when we have a single characteristic root, we use GS = (A1+A2n)α^n Also, for a certain scenario we use G.S = A1(α)^n.
Can anyone please tell me if we have any other formula's as well that we use to find General Solution(G.S) and for what scenario we need to use what formula.
Cheers!
This is a generic scenario for homogeneous linear recurrence relations with constant coefficients and it is considered in details in Wikipedia, see this” section.