Practice - Step 2: Guess the Form of the Particular Integral
Enroll to start learning
You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.
Practice Questions
Test your understanding with targeted questions
What is the trial solution if f(x) = sin(3x)?
💡 Hint: Remember it's sine and cosine.
If f(x) = 5x^2 + 3x, what's the trial solution?
💡 Hint: This is a polynomial function.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What is the initial guess for the particular integral of e^(3x)?
💡 Hint: Think of the function form.
True or False: The trial solution needs to be modified if it overlaps with the complementary function.
💡 Hint: Consider the implications of having the same terms.
1 more question available
Challenge Problems
Push your limits with advanced challenges
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.
Given y'' + y = 4sin(x) + e^(2x), determine the adjustments needed for your trial solutions.
💡 Hint: Focus on function types appearing in y_c.
Get performance evaluation
Reference links
Supplementary resources to enhance your learning experience.