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    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
    please help?
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    So, have you not been shown how to do this in lectures? In the same way as putting y=e^{\lambda t} into the 2nd order differential equation a\frac{d^2y}{dx^2}+b\frac{dy}{dx  }+c = 0 has solutions if lambda satisfies a\lambda^2 + b\lambda + c = 0, with a difference equation, put y=\lambda^t and substitute in to get a quadratic equation in lambda.
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    (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
    please help?
    You can solve them quite like second order differential equations with constant coefficients. First you have to find an eigenfunction (in this case, u_n = \lambda^n 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 3+4n^2, so you need to find the equivalent of the particular integral, by substituting, say, u_n = An^2 + Bn + C and comparing coefficients. Then you add the two together and hey presto.
 
 
 
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Updated: January 22, 2010
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