Practice Overview Of Linear Non-homogeneous Differential Equations (7.1) - Solution by Undetermined Coefficients

Practice: Overview of Linear Non-Homogeneous Differential Equations

Lesson 7.1Solution by Undetermined Coefficients

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11 questions

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6 sample questions

Question 1.
Define a linear non-homogeneous differential equation.
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Think about the general form with a forcing function.
Question 2.
What are the two parts of the general solution?
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Consider what each part represents.
3Question 3.
What is a linear non-homogeneous differential equation?
- An equation with no forcing function
- An equation with a non-zero term
- An equation with constant coefficients only
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Look for the term that differentiates it from homogeneous equations.
4Question 4.
True or False: The particular solution is only relevant for specific standard forms of forcing functions.
- True
- False
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Remember the types of functions we can use.
Question 5.
Given the differential equation $y'' + 4y = e^{-x}$ , determine the complementary function and apply the method of undetermined coefficients to find the particular solution.
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Don't forget to check the roots of the auxiliary equation!
Question 6.
For $y'' + 3y' + 2y = x^2 + e^x$ , solve for the complementary function and particular solutions for both terms.
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Remember the specific forms for your guesses!

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