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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Solve the equation d²y/dx² + 5y = 0. What type of roots do you expect?
💡 Hint: Use the auxiliary equation.
Question 2
Easy
What is the general solution when you have real distinct roots?
💡 Hint: Recall the roots format.
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 form does a second-order linear homogeneous ODE take?
- dy/dx + py + q = 0
- d²y/dx² + p dy/dx + qy = 0
- d²y/dx² = 0
💡 Hint: Identify the equality to zero.
Question 2
Does the general solution of a second-order ODE have arbitrary constants?
- True
- False
💡 Hint: Think about the roots of the auxiliary equation.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given the equation d²y/dx² + 10 = 0, derive the solution and determine the type of roots.
💡 Hint: Convert the equation into auxiliary form.
Question 2
For d²y/dx² + 8dy/dx + 16y = 0, prove that the roots are repeated and write the general solution.
💡 Hint: Look at the discriminant to confirm root multiplicity.
Challenge and get performance evaluation