Practice Solved Exercises - 2.10 | 2. Homogeneous Linear Equations of Second Order | Mathematics (Civil Engineering -1)
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Solved Exercises

2.10 - Solved Exercises

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Practice Questions

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Question 1 Easy

Solve the equation d²y/dx² + 4y = 0.

💡 Hint: Look for the characteristic roots involved.

Question 2 Easy

What form of solution corresponds to repeated roots?

💡 Hint: Consider the multiplicity of the roots.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What does the auxiliary equation allow us to find?

Roots of the equation
Boundary conditions
Specific functions

💡 Hint: It relates to solving the differential equation.

Question 2

True or False: Complex roots yield exponential solutions.

True
False

💡 Hint: Consider the form of the solutions for oscillatory systems.

2 more questions available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Solve the differential equation d²y/dx² - 6dy/dx + 9y = 0 and interpret the solution.

💡 Hint: Identify roots of the auxiliary equation first.

Challenge 2 Hard

If we have a structure modeled by the equation d²y/dx² + 8dy/dx + 16y = 0, find the general solution.

💡 Hint: Look at the discriminant for root types.

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