Practice Case 1: Repeated Roots And Duplication (7.7.1) - Solution by Undetermined Coefficients

Practice: Case 1: Repeated Roots and Duplication

Lesson 7.7.1Solution by Undetermined Coefficients

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6 sample questions

Question 1.
What should you do if the trial solution overlaps with the complementary function?
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Think about how many times the term appears in the complementary function.
Question 2.
Define repeated roots.
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Consider what happens to solutions when roots aren't distinct.
3Question 3.
What is the purpose of modifying a trial function in the method of undetermined coefficients?
- To ensure duplication is eliminated.
- To make calculations easier.
- To change the forcing function.
- It serves no particular purpose.
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Consider the role of the complementary function.
4Question 4.
True or False: Duplication can occur only with polynomial functions.
- True
- False
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Think about other functional forms like exponentials.
Question 5.
Given the differential equation y'' - 6y' + 9y = 12e^(3x), identify the trial solution and show your work.
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Evaluate the characteristic equation carefully.
Question 6.
Solve for y in the equation y'' + 4y = 2sin(2x) and adjust the trial solution accordingly.
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Determine the complementary function first.

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