Difference equation

[haoku]

1. The problem statement, all variables and given/known data
Given difference equation
T(a+2)-7T(a+1) +6T(a)= 6f
Find the general solution of this equation

2. Relevant equations
I have found the auxiliary equation be
A(1)^n+B(6)^n
But seems can't find the particular solution of that question.
Is it impossible to do this question?


3. The attempt at a solution

[tiny-tim]

Hi haoku! :smile:
T(a+2)-7T(a+1) +6T(a)= 6f

What's f? :confused:

[HallsofIvy]

f is a constant? Then "trying" a constant as solution won't work because a constant already satisfies the homogeneous equation (n0= 1). Try T(n)= Cn as a solution and determine C.

[haoku]

Sorry this is 6a

[tiny-tim]

Sorry this is 6a

ah! :biggrin:

in that case, try a polynomial in a. :smile: