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**dunsta** Can anybody point me towards a similar problem with a solution. So far in Discrete maths I have had the best results from looking at a problem with a soution and then working out the hows and whys, I have read my notes on this topic over and over but they are long winded explanations in words, with no examples.

So if any one can point me to a similar problem/exercise I would be appreciative. At the moment I seem to be lost with this problem.

$\displaystyle a_{n+2} - 2a _{n+1} -63a_{n} = 64n$, n>= 0 with $\displaystyle a_{0} = 0 a_{1} = 7$

(x-9)(x+7) = 0

x=9, x=-7 <---is this part correct?

$\displaystyle u_{n} = A*9^n + B * -7^n$ for arbitrary constants A and B Mr F says: To check if it's correct, substitute it into the **homogenous** difference equation. Does it work? (Do you understand the thinking behind what you have done above?)

RHS

64n =

$\displaystyle V_{n} = (1^n) * (C_{n} + D) = (C_{n} + D)$ <-- is this correct?? Mr Fantastic is this the particular solution you refer to that should be $\displaystyle a_{n} = -n$ Mr F says: Yes.

$\displaystyle A9^n + B(-7)^n + n - 64$ for arbitrary constants A and B

$\displaystyle a_{0} =0 = A * 9^0 + B*-7^0 + 0 -64$

$\displaystyle a_{1} = 7 = A * 9^1 + B*-7^1 + 1 -64$ <-- I think my goal is to try and find A and B for these expressions