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# second order difference equations help? watch

1. find general solutions to the following second order difference equations:
a) Un+2 - 10Un+1 + 24Un = 0

b) Un + 14Un-1 + 49Un-2 = 3 + 4n^2
2. So, have you not been shown how to do this in lectures? In the same way as putting into the 2nd order differential equation has solutions if lambda satisfies , with a difference equation, put and substitute in to get a quadratic equation in lambda.
3. (Original post by Bec..)
find general solutions to the following second order difference equations:
a) Un+2 - 10Un+1 + 24Un = 0

b) Un + 14Un-1 + 49Un-2 = 3 + 4n^2
You can solve them quite like second order differential equations with constant coefficients. First you have to find an eigenfunction (in this case, will normally do the trick) and then substitute it into the homogeneous equation (i.e. with 0 on the RHS) to find a complimentary function. For (b) there is a forcing term , so you need to find the equivalent of the particular integral, by substituting, say, and comparing coefficients. Then you add the two together and hey presto.

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Updated: January 22, 2010
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