Practice Step 3: Modify Trial Solution If Needed (7.3.3) - Solution by Undetermined Coefficients

Practise this section

8 questions

Flashcard drill
2 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
Sign up to start the exercise
Quiz
2 questions · about 1 min · pass mark 70%. Hints available.
Sign up to start the quiz

6 sample questions

Question 1.
Define what is meant by a trial solution in the context of differential equations.
Show hintHide hint
Think about what kind of solution we are looking for.
Question 2.
Explain the repetition rule briefly.
Show hintHide hint
Consider why duplications in solutions are problematic.
3Question 3.
What is the purpose of modifying the trial solution?
- To eliminate duplication
- To change the function type
- To complicate calculations
Show hintHide hint
Think about the accurate formation of solutions.
4Question 4.
When would you use 'x^2' in your modifications?
- True
- False
Show hintHide hint
Think about the frequency of terms.
Question 5.
Given the equation y'' + y = xe^x, identify the complementary function and discuss how the trial solution should be selected and modified.
Show hintHide hint
Identify components in your solutions carefully.
Question 6.
Solve y'' - y = e^(2x) + xe^(2x) requiring careful observation of repetitions in solutions.
Show hintHide hint
Always check for repeated elements in your functions.

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