Practice Non-homogeneous Systems Of Differential Equations (6.7) - Non-Homogeneous Equations

Practice: Non-Homogeneous Systems of Differential Equations

Lesson 6.7Non-Homogeneous Equations

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8 questions

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6 sample questions

Question 1.
Define a non-homogeneous differential equation.
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Think about what differentiates it from a homogeneous system.
Question 2.
What are eigenvalues?
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Remember, they are linked to the response characteristics of the system.
3Question 3.
What distinguishes a non-homogeneous system from a homogeneous system?
- It has no external forces
- It includes external terms
- It is always stable
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Think about what forces could be acting on a system.
4Question 4.
True or False: Eigenvalues can indicate the stability of a system.
- True
- False
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Reflect on what eigenvalues represent in the context of systems.
Question 5.
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.
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Look for the determinant being equal to zero.
Question 6.
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.
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Identify the non-homogeneous terms first!

4 more questions in this section. Enroll free to practise them all.