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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define a differential equation.
💡 Hint: Think about functions and their rates of change.
Question 2
Easy
What is the order of the equation d²y/dx² + y = 0?
💡 Hint: Identify the highest derivative in the equation.
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 defines a linear differential equation?
- Dependent variable is squared
- Derivatives are to the first power
- Variables are multiplied together
💡 Hint: Focus on the definition of 'linearity'.
Question 2
True or False: A second-order linear DE can be homogeneous.
- True
- False
💡 Hint: Remember the differences between homogeneous and non-homogeneous forms.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given the second-order DE d²y/dx² + 3dy/dx + 2y = 0, find the general solution.
💡 Hint: Identify the roots using factoring.
Question 2
For the non-homogeneous equation d²y/dx² - y = e^x, derive the particular solution.
💡 Hint: Use the method of undetermined coefficients.
Challenge and get performance evaluation