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Last effort on this difference equation..

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Hi.. Just a last resort effort to see if anyone can shed some light on how to solve this; some guidelines would be very much appreciated.. I have to find the general solution of this difference equation: Yn+4 - 6Yn+3 + 14Yn+2 - 14Yn+1 + 5Yn = 1 .. where n+4, n+3, .. are subscripts of Y. I realise to do this you substitute L^n for Yn (where L = lambda) and find an auxiliary equation to find roots, but all the examples we''ve been given deal with equations of the form Yn+2 + Yn+1 + Yn , which is fairly easy to find the roots for. But how can I find the roots for the above 4th order equation? Should I be using Newtons method for this? If anyone can help that would be grand

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There is such a thing as a closed-form solution to find the roots of a quartic expression. Try looking up the "quartic formula".

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You probably have to find the roots "creatively", using exp(lambda*x), if it''s HW. Or use an iterative method like Newton. What have you learned in this course?

Remember, though, that the solution to the inhomogeneous equation is the general solution to the homogeneous one + one specific solution of the inhomogeneous equation (that you have to find creatively again, AFAIK).

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