Practice Illustrative Examples (7.4) - Solution by Undetermined Coefficients
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Illustrative Examples

Practice - Illustrative Examples

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Practice Questions

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Question 1 Easy

What is the complementary function for y′′ + 4y = 0?

💡 Hint: Use the auxiliary equation approach.

Question 2 Easy

What is a typical guess for the particular integral if f(x) = e^(3x)?

💡 Hint: Think about the form of the non-homogeneous term.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What does the method of undetermined coefficients help us find?

Complementary Function
Particular Integral
General Solution

💡 Hint: Remember the names of different components in a solution.

Question 2

True or False: The trial solution is always unique in the method of undetermined coefficients.

True
False

💡 Hint: Think about how we adjust our trial solutions.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Given the differential equation y′′ + 5y′ + 6y = e^(-3x), find the general solution.

💡 Hint: Start by solving the homogeneous part, then adjust your guess for y_p.

Challenge 2 Hard

How would you solve the equation y′′ + 4y = x^2 cos(2x) using the method of undetermined coefficients?

💡 Hint: Remember to check for duplication with the complementary function.

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