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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the characteristic equation derived from the equation d²y/dx² - 3dy/dx + 2y = 0?
💡 Hint: Only consider the coefficients of the original equation.
Question 2
Easy
What happens when the discriminant is negative?
💡 Hint: Think about how the roots can affect the solution's behavior.
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 characteristic equation derived from d²y/dx² + 2dy/dx + y = 0?
- r² + 2r + 1 = 0
- r² - 2r + 1 = 0
- r² + 2r - 1 = 0
💡 Hint: Look carefully at how the differential equation coefficients correspond to terms in the characteristic equation.
Question 2
If the discriminant is zero, what type of roots do we have?
- True
- False
💡 Hint: Think about what this implies for the general solution.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Derive the general solution for the ODE d²y/dx² - 6dy/dx + 9y = 0.
💡 Hint: Use the quadratic formula and remember the implications of multiple roots.
Question 2
For the differential equation y'' + 4y' + 20y = 0, find and analyze the nature of its roots and the general solution.
💡 Hint: Identify the real and imaginary parts carefully to construct the final solution.
Challenge and get performance evaluation