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
Define a non-homogeneous differential equation.
💡 Hint: Think about what differentiates it from a homogeneous system.
Question 2
Easy
What are eigenvalues?
💡 Hint: Remember, they are linked to the response characteristics of the system.
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 distinguishes a non-homogeneous system from a homogeneous system?
- It has no external forces
- It includes external terms
- It is always stable
💡 Hint: Think about what forces could be acting on a system.
Question 2
True or False: Eigenvalues can indicate the stability of a system.
- True
- False
💡 Hint: Reflect on what eigenvalues represent in the context of systems.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Analyze the following system and determine the eigenvalues: $$\frac{dx}{dt} = x + 2y; \frac{dy}{dt} = -3x + 4y$$. Find the solution to the homogeneous part.
💡 Hint: Look for the determinant being equal to zero.
Question 2
Given the non-homogeneous equation $$\frac{dx}{dt} = 2x + 3y + \cos(t); \frac{dy}{dt} = -xy + 4y + e^{-t}$$, identify the external terms and solve the system.
💡 Hint: Identify the non-homogeneous terms first!
Challenge and get performance evaluation