Practice Finding The Particular Integral (6.3) - Non-Homogeneous Equations

Practice: Finding the Particular Integral

Lesson 6.3Non-Homogeneous Equations

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9 questions

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3 questions · about 2 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
What is the purpose of finding the particular integral in a differential equation?
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Think about both parts of the solution.
Question 2.
When can you use the method of undetermined coefficients?
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What types of functions do you see in the non-homogeneous term?
3Question 3.
What is the key purpose of finding the particular integral in a non-homogeneous equation?
- To determine the complementary solution
- To find a specific solution to the non-homogeneous part
- To simplify the equation
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Focus on the role of the PI.
4Question 4.
The method of variation of parameters is used when the non-homogeneous term does not fit into standard types.
- True
- False
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Think about when we use different methods.
Question 5.
For the non-homogeneous equation y'' + 6y' + 9y = 3e^{-3x}, find the PI using the method of undetermined coefficients.
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Identify if your guessed function overlaps with the complementary function.
Question 6.
Solve the system described by y' = 3x + 4y + sin(t), y = -4x + 3y + e^t using variation of parameters.
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Look for linearly independent solutions.

5 more questions in this section. Enroll free to practise them all.