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 January 28th, 2012, 11:24 PM #1 Newbie   Joined: Jan 2012 Posts: 5 Thanks: 0 changing difference equation I have to change this systems of difference equation to a single higher order equation. The answer is What I did so far was set it equal to zero and got this: I am not sure what to do after. I think I am supposed to find the characteristic equation but my equation doesn't look like a polynomial. Can someone help me figure this out please? Thank you for your time! January 28th, 2012, 11:27 PM #2 Newbie   Joined: Jan 2012 Posts: 5 Thanks: 0 Re: changing difference equation Whoops. I made a mistake on the second equation. It is January 29th, 2012, 12:01 AM #3 Senior Member   Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 522 Math Focus: Calculus/ODEs Re: changing difference equation We are given: (1) (2) Method 1: Taking (2) and replacing n with n + 1 gives: Using (1), substitute for : Solving (2) for and substituting, we then get: Now we have a linear homogeneous recurrence, whose associated characteristic equation is: Thus, we find the closed-form for is: where A and B are arbitrary constants. Method 2: Taking (1) and replacing n with n + 1 gives: Using (2), substitute for : Solving (1) for and substituting, we then get: Now we have a linear homogeneous recurrence, whose associated characteristic equation is: Thus, we find the closed-form for is: where A and B are arbitrary constants. Tags changing, difference, equation Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post binarygoodmathpoor Calculus 1 February 12th, 2014 07:33 AM capea Complex Analysis 3 September 11th, 2013 01:09 AM bilano99 Calculus 4 March 22nd, 2012 04:58 PM uterfor86 Applied Math 1 January 15th, 2012 10:38 PM BlackKnight Applied Math 0 March 15th, 2009 11:25 AM

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