Enrol to start learning

Reading is open to everyone. Enrolling is free, and it is what unlocks the audio lessons, practice tests and progress tracking.

8. Solution by Variation of Parameters

This section
Practice test
10 questions on this section. Wrong answers show you what to read again.
Sign up to take it
Whole chapter
Revision test
Mixed questions from across the chapter. Your answers get marked.
Sign up to take it
Quick
Flashcard drill
2 cards from this lesson. Good the night before a test.

1.
What is a non-homogeneous differential equation?
Hint
Consider how it differs from a homogeneous equation.
2.
Describe the Wronskian.
Hint
Think of how it’s constructed using y and its derivatives.
3.
What does variation of parameters allow us to do?
- Find solutions to polynomial equations.
- Obtain particular solutions to non-homogeneous differential equations.
- Calculate integrals directly.
Hint
Think about the applicability of this method.
4.
True or False: The Wronskian can be zero for independent solutions.
- True
- False
Hint
Remember what linear independence implies.
5.
A beam is subject to a varying load modeled by g(x) = x^2. Derive the differential equation using variation of parameters and find the particular solution.
Hint
Focus on computing the Wronskian accurately.
6.
Describe the limitations of variation of parameters and when you might prefer another method.
Hint
Think about the types of functions you can use.

Exercises

Total Questions

Estimated Time

4 min

Passing Score

70%

4 more questions available

Total Questions

Estimated Time

4 min

Passing Score

70%

Get your answers marked and your progress tracked

Total Questions

Estimated Time

4 min

Passing Score

70%