Solve Difference Equation | General Solution | No Particular Solution

[haoku]

Homework Statement

Given difference equation
T(a+2)-7T(a+1) +6T(a)= 6f
Find the general solution of this equation

Homework 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?

The Attempt at a Solution

 

[tiny-tim]

Hi haoku!

T(a+2)-7T(a+1) +6T(a)= 6f

What's f?

 

[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!

in that case, try a polynomial in a. ​