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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the trial solution if f(x) = sin(3x)?
💡 Hint: Remember it's sine and cosine.
Question 2
Easy
If f(x) = 5x^2 + 3x, what's the trial solution?
💡 Hint: This is a polynomial function.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What is the initial guess for the particular integral of e^(3x)?
- Ae^(3x)
- Ax*e^(3x)
- A*cos(3x) + B*sin(3x)
💡 Hint: Think of the function form.
Question 2
True or False: The trial solution needs to be modified if it overlaps with the complementary function.
- True
- False
💡 Hint: Consider the implications of having the same terms.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Solve the differential equation y'' - 3y' + 2y = e^(x) + x. Find the particular integral with appropriate adjustments.
💡 Hint: Review the forms of f(x) and identify overlaps.
Question 2
Given y'' + y = 4sin(x) + e^(2x), determine the adjustments needed for your trial solutions.
💡 Hint: Focus on function types appearing in y_c.
Challenge and get performance evaluation