Practice Methods Of Finding Particular Solution (1.7) - Linear Differential Equations

Practice: Methods of Finding Particular Solution

Lesson 1.7Linear Differential Equations

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8 questions

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6 questions · about 4 min · pass mark 70%. Hints available.
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2 questions · about 1 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
Using the Method of Undetermined Coefficients, what form would you assume for R(x) = 3x^2?
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Consider the degree of the polynomial when making your assumption.
Question 2.
True or False: The Method of Variation of Parameters requires the solution of a homogeneous equation to find u1 and u2.
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Recall the relationship between complementary and particular solutions.
3Question 3.
What is the Method of Undetermined Coefficients used for?
- Finding homogeneous solutions
- Finding particular solutions
- Both
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Think about what type of solution each method aims to find.
4Question 4.
True or False: The Method of Variation of Parameters can be used when R(x) has any form.
- True
- False
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Consider the limitations of the Method of Undetermined Coefficients.
Question 5.
Given the non-homogeneous equation y'' + y = 2e^x, solve for the particular solution using the Method of Undetermined Coefficients.
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What happens when you plug your y_p form back into the original equation?
Question 6.
For the differential equation y'' + 3y' + 2y = cos(x), apply the Method of Variation of Parameters.
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Focus on the relationships established from your homogeneous solution!

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