Practice Solving the Homogeneous Part - 6.2 | 6. Non-Homogeneous Equations | Mathematics (Civil Engineering -1)
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6.2 - Solving the Homogeneous Part

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What is the general form of the auxiliary equation for a second-order linear homogeneous differential equation?

💡 Hint: Remember, it relates to the coefficients of the differential equation.

Question 2

Easy

What is the form of the complementary function if there are distinct real roots?

💡 Hint: Think about how you combine the solutions of each root.

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 the complementary function take for distinct real roots?

  • y_h = (C_1 + C_2x)e^{r x}
  • y_h = C_1 e^{r_1 x} + C_2 e^{r_2 x}
  • y_h = e^{αx}(C_1 cos(βx) + C_2 sin(βx))

💡 Hint: Focus on how these solutions are articulated.

Question 2

True or False: The form of the complementary function when roots are complex involves trigonometric functions.

  • True
  • False

💡 Hint: Recall the connection of sin and cos with imaginary numbers.

Solve 1 more question and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

Solve the differential equation d²y/dx² - 5dy/dx + 6y = 0 and find the complete complementary function.

💡 Hint: Start by setting the roots using the quadratic formula.

Question 2

For the equation d²y/dx² + 4y = 0, find the roots and formulate the complementary function.

💡 Hint: Determine the imaginary components of the roots carefully.

Challenge and get performance evaluation