2.9 - Exercises
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Practice Questions
Test your understanding with targeted questions
Solve the equation d²y/dx² + 5y = 0. What type of roots do you expect?
💡 Hint: Use the auxiliary equation.
What is the general solution when you have real distinct roots?
💡 Hint: Recall the roots format.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What form does a second-order linear homogeneous ODE take?
💡 Hint: Identify the equality to zero.
Does the general solution of a second-order ODE have arbitrary constants?
💡 Hint: Think about the roots of the auxiliary equation.
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Challenge Problems
Push your limits with advanced challenges
Given the equation d²y/dx² + 10 = 0, derive the solution and determine the type of roots.
💡 Hint: Convert the equation into auxiliary form.
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.
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