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June 17th, 2013, 06:24 AM   #1
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Solving Recurrence equation

Hey, so I have:



I also have the initial conditions, a0 = 5 and a1 = 4.

I have to 'solve' it but I having issues.

Answer for general solution is:

And it then applies initial conditions to get solution:

My attempt so far has been unsuccessful. I know we use the homogenous equation but I cannot figure out how. Any help? Thanks!
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June 17th, 2013, 08:28 AM   #2
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Re: Solving Recurrence equation

We first solve the associated homogenous equation:



which has the auxiliary equation:



Hence, a general solution to the homogeneous equation is:



Since the inhomogeneous term is , we seek a particular solution of the form:



where the constants and are to be determined. Substituting this expression for into the recursion, we find:









Equating coefficients, we find:





Thus, we have found:



and so:



Now, we may determine the parameters from the given initial values:





Solving this linear 2X2 system, we find:



and thus we finally have:

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June 17th, 2013, 01:20 PM   #3
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Re: Solving Recurrence equation

Nicely done!
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