Question

What is the general form of the solutions of a linear homogenous recurrence
relation if its characteristic equation has the roots −1, −1, −1,2,2,5,5,7?

Answer 1

The characteristic equation has the factorization:
\[(x+1)^3(x-2)^2(x-5)^2(x-7)\]
so you have, as a general solution,
\[a_n=(k_1+k_2n+k_3n^2)(-1)^n+(k_4+k_5n+k_6n^3)2^n+(k_7+k_8n)5^n+k_97^n\]

Answer 2

Oh my. That seems so simple now. Thank you!

Answer 3

You're welcome!