6.7 - Non-Homogeneous Systems of Differential Equations
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Practice Questions
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Define a non-homogeneous differential equation.
💡 Hint: Think about what differentiates it from a homogeneous system.
What are eigenvalues?
💡 Hint: Remember, they are linked to the response characteristics of the system.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What distinguishes a non-homogeneous system from a homogeneous system?
💡 Hint: Think about what forces could be acting on a system.
True or False: Eigenvalues can indicate the stability of a system.
💡 Hint: Reflect on what eigenvalues represent in the context of systems.
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Challenge Problems
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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.
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!
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