Solve Difference Equation | General Solution | No Particular Solution

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Homework Help Overview

The discussion revolves around a difference equation given by T(a+2) - 7T(a+1) + 6T(a) = 6f, with the goal of finding its general solution. Participants are exploring the nature of the function f and its implications on the solution process.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants are questioning the nature of the function f, with one suggesting that if f is a constant, it complicates finding a particular solution. Another participant proposes trying a polynomial solution based on the clarification of f.

Discussion Status

The discussion is ongoing, with participants actively questioning assumptions about the function f and exploring different forms of potential solutions. There is no clear consensus yet, but suggestions for alternative approaches are being made.

Contextual Notes

There is some ambiguity regarding the definition of f, which is crucial for determining the approach to the problem. The participants are also navigating the implications of the homogeneous equation in their attempts to find a particular solution.

haoku
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Homework Statement


Given difference equation
T(a+2)-7T(a+1) +6T(a)= 6f
Find the general solution of this equation

Homework Equations


I have found the auxiliary equation be
A(1)^n+B(6)^n
But seems can't find the particular solution of that question.
Is it impossible to do this question?


The Attempt at a Solution

 
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Hi haoku! :smile:
haoku said:
T(a+2)-7T(a+1) +6T(a)= 6f

What's f? :confused:
 
f is a constant? Then "trying" a constant as solution won't work because a constant already satisfies the homogeneous equation (n0= 1). Try T(n)= Cn as a solution and determine C.
 
Sorry this is 6a
 
haoku said:
Sorry this is 6a

ah! :biggrin:

in that case, try a polynomial in a. :smile:​
 

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