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# solving non-homogeneous difference equations watch

a)

I don't know how to find the characteristic polynomial for this, I get lambda = 1/2^n

b)

for this, I did the characteristic polynomial: lambda = 1/4 and lambda = 1

then when I try and subst. into the original, I get M_1 = 31/3 but M_0 cancels out.

I know I need to find A and B

c)

I'm assuming this is similar to b) but what would P(n) be?

Thanks
2. (Original post by ~tis)
...

Thanks
I can look at this tomorrow evening (bedtime soon) but would you be as kind as to post a photo of the question please
3. (Original post by TeeEm)
I can look at this tomorrow evening (bedtime soon) but would you be as kind as to post a photo of the question please
sorry just seen this
Attached Images

4. (Original post by ~tis)
sorry just seen this
I need to look up how to do the first one

the second one I just did, bit messy but standard
the "complimentary function" is A + B x 4n (no quarter)

The third one I might try it tonight if I get a minute otherwise on Monday
5. (Original post by ~tis)
sorry just seen this
I just did the third one (also ok).
6. (Original post by TeeEm)
I just did the third one (also ok).
thanks going to try now.

yeah, the first one's got me really stuck because of it being raised to n
7. (Original post by ~tis)
thanks going to try now.

yeah, the first one's got me really stuck because of it being raised to n
I have written neat solutions to the last 2, so if you get stuck yell....

The first one I will need to look up a few things before I attempt it which will now be on Monday

all the best
8. (Original post by TeeEm)
I have written neat solutions to the last 2, so if you get stuck yell....The first one I will need to look up a few things before I attempt it which will now be on Mondayall the best

I still can't get the answer for b).

I have G(n) = A + 4Bn and P(n) = nM_0 + M_1n^2

Then do I subst. P(n) into the original equation?
i.e.

but then I get M_1 = 31/3

and I don't know what to do after this
9. (Original post by ~tis)
I still can't get the answer for b).

I have G(n) = A + 4Bn and P(n) = nM_0 + M_1n^2

Then do I subst. P(n) into the original equation?
i.e.

but then I get M_1 = 31/3

and I don't know what to do after this
I just finished teaching
Give me a while to eat and I will post (b)
10. here is question 2
Attached Images

11. (Original post by TeeEm)
here is question 2
thank you
12. (Original post by ~tis)
thank you
no worries...
13. here is Q3
I must remember to look at Q1
Attached Images

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