Hey ineedalottahelp.
What do your notes give you in terms of formulae and theorems for this kind of problem?
So I have an assignment and i'm having trouble doing it. The question in hand.
1. a) Solve the recurrence relation:
a_{n} = 4a_{n-1} + 5a_{n-2 }+ (-1)^{n}(36n - 6) + ( (-1)^{n}(11n - 10) / 2^{n} )
where a_{0 }= 1 and a_{1} = 0.5
I got as far as to find the characteristic solution for the homogeneous part but have no clue how to find the particular solution for the next part.
a_{n} = 4_{n-1} + 5a_{n-2}
x^{2} -4x - 5
(x - 5)(x + 1)
b_{n} = C_{1}5^{n} + C_{2}(-1)^{n}
b) Write down the close form of the generating function of the sequence a_{n. }Maybe a hint to which direction I should go?
Thank you!
Basically they've told us to find b_{n }
Find p_{n} for the constant part
Combine p_{n} and b_{n}
Sub in initial conditions and solve for constant variables in p_{n }
Where i'm at with finding p_{n}
4( ((-A^{n-1})(B(n-1)-C) + ((-A^{n-1})(C(n-1)-D)(E2^{n-1})) ) + 5 ( ((A^{n-2})(B(n-2)-C) + ((-A^{n-2})(C(n-2)-D)(E2^{n-2})) ) + (-1)^{n}(36n - 6) + ( (-1)^{n}(11n - 10) / 2^{n} )
But I have no clue if that's the right direction.