Practice Methods For Finding Particular Solutions (19.2.4) - Lecture -39: Solving Linear Non- Homogeneous Recurrence Equations

Practice: Methods for Finding Particular Solutions

Lesson 19.2.4Lecture -39: Solving Linear Non- Homogeneous Recurrence Equations

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6 sample questions

Question 1.
Define what a non-homogeneous recurrence equation is?
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Think of how it differs from a homogeneous one.
Question 2.
What is the associated homogeneous relation?
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Recall how we simplify the equation.
3Question 3.
What is the first step to solve a linear non-homogeneous recurrence equation?
- Find the roots of F(n)
- Form the associated homogeneous relation
- Guess the particular solution
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Think about what we do to simplify the original equation.
4Question 4.
True or False: The particular solution satisfies only the homogeneous part of the recurrence.
- True
- False
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Recall the components of a particular solution.
Question 5.
Given the recurrence relation a_n = 4a_(n-1) + 2n, derive the general solution.
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Remember the steps of chopping off and combining solutions.
Question 6.
If the recurrence is defined as a_n = 5a_(n-1) + 7, determine the structure of your particular solution based on the roots identified.
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Think about what it means when the constant is not a root of the characteristic equation.

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