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# Second Order Difference Equation Watch

1. How do I solve c_n+2=c_n(a+b^2) where a and b are constants.
2. I take it a and b are constant (or at least independent of n)?

in which case, let and solve for . You'll get two non-zero roots , so then , and so on... all the standard method.
3. (Original post by nuodai)
I take it a and b are constant (or at least independent of n)?

in which case, let and solve for . You'll get two non-zero roots , so then , and so on... all the standard method.

So I get

But I can't see how to solve this :P
4. (Original post by Jooeee)
So I get

But I can't see how to solve this :P
Factorise it. Hint: look for a common factor.
5. (Original post by nuodai)
Factorise it. Hint: look for a common factor.

So

so
6. (Original post by Jooeee)

So

so
Yarp.
7. (Original post by nuodai)
Yarp.
Ok thanks, I had got this solution before. So then my general solution would be

But it says to show that the general solution is

But I can't see where this comes from at all.
8. (Original post by Jooeee)
Ok thanks, I had got this solution before. So then my general solution would be

It would actually be .

(Original post by Jooeee)
But it says to show that the general solution is

But I can't see where this comes from at all.
I would expect that would be the solution to , which definitely isn't what you said. Are you sure you copied out the question correctly? If not, it's probably a typo somewhere in the question.

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