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I am trying to explicitly solve [ if possible and if the solution exists ] a second order non-linear difference equation of the form :

$ a _ {n+2} ^2 + a_{n} ^2 + K = \lambda a_{n+1} $, where K and $\lambda$ are known positive constants ( assume K =10 and $\lambda =5 $ if you like ).

Is there any reference for it ? Or any paper that talks about the solution ?

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For existence, have you tried numerical experimentation? –  S. Carnahan Nov 28 '10 at 15:59
    
No, actually I am not aware of how to do that, but could you suggest a reference or so ? I study pure Mathematics, so I don't know much about numerical solutions etc . The difference equation arose part of my research. –  Analysis Now Nov 29 '10 at 4:51

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