Professional Courses
Industry-relevant training in Business, Technology, and Design to help professionals and graduates upskill for real-world careers.
Categories
Interactive Games
Fun, engaging games to boost memory, math fluency, typing speed, and English skills—perfect for learners of all ages.
Typing
Memory
Math
English Adventures
Knowledge
Enroll to start learning
You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.
Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the general form of a homogeneous equation?
💡 Hint: Remember it involves derivatives of the function y.
Question 2
Easy
Define what an auxiliary equation is.
💡 Hint: Think of it as the characteristic polynomial derived from the differential equation.
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 homogeneous differential equation take?
- a dy/dx + by = 0
- a d²y/dx² + b dy/dx + cy = 0
- b dy/dx + c = 0
💡 Hint: Consider the derivatives involved in the equation.
Question 2
True or false: The roots of the auxiliary equation can be complex.
- True
- False
💡 Hint: Think about the types of solutions we discussed.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Find the general solution for the differential equation d²y/dx² - 4dy/dx + 4y = 0 and discuss the significance of your results.
💡 Hint: Consider how repeated roots change the form of the solution.
Question 2
Solve the equation d²y/dx² + 2dy/dx + 5y = 0, derive the general solution and reflect on its application context in engineering.
💡 Hint: Use the quadratic formula on the auxiliary equation to find roots.
Challenge and get performance evaluation