Practice Principle Of The Variation Of Parameters (8.2) - Solution by Variation of Parameters

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6 sample questions

Question 1.
Define a non-homogeneous equation.
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Think about what extra terms might look like.
Question 2.
What is the form of a homogeneous solution?
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Consider the constant coefficients for a family of solutions.
3Question 3.
What is the first step in the Variation of Parameters?
- Identify g(x)
- Differentiate y_h
- Assume a form for y_p
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Think about how we structure our assumptions.
4Question 4.
True or False: The Variation of Parameters can only handle polynomial forcing functions.
- True
- False
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Consider the flexibility of the method.
Question 5.
Solve the following differential equation using the variation of parameters: y'' + 2y' + y = e^x.
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Remember to check your integration carefully for any retries.
Question 6.
Using the Variation of Parameters, show how to derive a particular solution for y'' - 4y = sin(x).
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Start fresh with the Wronskian calculation and methodically go through each step.

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