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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Solve the equation d²y/dx² - 2dy/dx + y = 0.
💡 Hint: Look for repeated roots in the auxiliary equation.
Question 2
Easy
Solve the equation d²y/dx² + 4y = 0.
💡 Hint: Check for complex roots in the auxiliary 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 is the general solution of d²y/dx² - 5dy/dx + 6y = 0?
💡 Hint: Derive it from the auxiliary equation.
Question 2
True or False: The general solution for repeated roots includes a linear term.
- True
- False
💡 Hint: Recall the formula for repeated roots.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Solve the differential equation d²y/dx² - 8dy/dx + 16y = 0 and analyze the implications of the solution.
💡 Hint: Pay attention to the nature of the roots and apply the correct form.
Question 2
Evaluate the equation d²y/dx² + 6dy/dx + 10y = 0, identify the nature of the roots, and provide the general solution.
💡 Hint: Utilize the quadratic formula and consider the implications of complex roots.
Challenge and get performance evaluation