Practice Conceptual Notes (6.9) - Non-Homogeneous Equations

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6 sample questions

Question 1.
What is the primary difference between homogeneous and non-homogeneous differential equations?
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Think about the presence or absence of external forces.
Question 2.
Define the term 'forcing function' in the context of differential equations.
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It's what pushes the system away from its natural response.
3Question 3.
What do non-homogeneous differential equations primarily model?
- Natural vibrations
- Forced systems
- Linear motion
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Think about how forces change the system's behavior.
4Question 4.
True or False: The method of undetermined coefficients can be applied to all types of forcing functions.
- True
- False
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Remember the limits of P.E.T.
Question 5.
Solve the non-homogeneous differential equation: y'' + 3y' + 2y = e^x.
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Start with characteristics before tackling the PI.
Question 6.
Using the method of variation of parameters, solve: y'' + y = sin(2x).
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Split the problem into manageable parts!

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