Practice Auxiliary Equation (AE) - 1.5.2 | 1. Linear Differential Equations | Mathematics (Civil Engineering -1)
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1.5.2 - Auxiliary Equation (AE)

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What is the form of the Auxiliary Equation derived from a second-order linear differential equation?

💡 Hint: What quadratic equation relates to the coefficients of the original differential equation?

Question 2

Easy

In which case do we use the solution form y = C₁e^(m₁x) + C₂e^(m₂x)?

💡 Hint: Think about how many different roots would provide different exponential terms.

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 first step in using the Auxiliary Equation to solve a second-order linear differential equation?

  • Solving for the roots directly
  • Forming the Auxiliary Equation
  • Applying initial conditions

💡 Hint: What kind of equation helps us find the roots?

Question 2

A differential equation with complex roots has solutions that involve which functions?

  • Exponential only
  • Sine and Cosine
  • None of the above

💡 Hint: Consider how oscillatory behavior is represented in solutions.

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Challenge Problems

Push your limits with challenges.

Question 1

Show that for the equation 2y'' - y' + 5y = 0, the roots of the Auxiliary Equation lead to an oscillatory solution. Determine the general solution.

💡 Hint: Calculate the discriminant first to find the nature of the roots.

Question 2

For the differential equation d²y/dx² + 2dy/dx + 5y = 0, find the roots of the Auxiliary Equation and describe the general behavior of the solution.

💡 Hint: Again, your first step should be to calculate the discriminant for classification.

Challenge and get performance evaluation