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June 17th, 2013, 06:24 AM  #1 
Newbie Joined: Apr 2013 Posts: 20 Thanks: 0  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! 
June 17th, 2013, 08:28 AM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs  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: 
June 17th, 2013, 01:20 PM  #3 
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  Re: Solving Recurrence equation
Nicely done!


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equation, recurrence, solving 
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