You are solving a 2x2 system of the form : PỸ + where P has constant entries with real different eigenvalues. s(t) = Decide which of the following statements is correct: I can find a particular solution using the undetermined coefficients method with a try function of the form Y(t) = sin(t)ā + cos I can find a particular solution using the undetermined coefficients method with a try function of the form Y(t) = (cos(t) + sin(t))ä I can only find the general solution for this problems using the Variation of Parameters method. Undetermined Coefficients won't work in this case. I can find the general solution using the undetermined coefficients method. To find the particular solution I should use a with a try function of the form Y(t) = sin(t)ā

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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You are solving a 2x2 system of the form:

\[ \vec{Y}' = P \vec{Y} + \begin{bmatrix} 0 \\ \cos(t) \end{bmatrix} \]

where \( P \) has constant entries with real different eigenvalues.

Decide which of the following statements is correct:

1. (Option): I can find a particular solution using the undetermined coefficients method with a try function of the form

   \[ \vec{Y}(t) = \sin(t)\vec{a} + \cos(t)\vec{b} \]

2. (Option): I can find a particular solution using the undetermined coefficients method with a try function of the form

   \[ \vec{Y}(t) = (\cos(t) + \sin(t))\vec{a} \]

3. (Option): I can only find the general solution for this problem using the Variation of Parameters method. Undetermined Coefficients won't work in this case.

4. (Option): I can find the general solution using the undetermined coefficients method. To find the particular solution I should use a try function of the form

   \[ \vec{Y}(t) = \sin(t)\vec{a} \]
Transcribed Image Text:You are solving a 2x2 system of the form: \[ \vec{Y}' = P \vec{Y} + \begin{bmatrix} 0 \\ \cos(t) \end{bmatrix} \] where \( P \) has constant entries with real different eigenvalues. Decide which of the following statements is correct: 1. (Option): I can find a particular solution using the undetermined coefficients method with a try function of the form \[ \vec{Y}(t) = \sin(t)\vec{a} + \cos(t)\vec{b} \] 2. (Option): I can find a particular solution using the undetermined coefficients method with a try function of the form \[ \vec{Y}(t) = (\cos(t) + \sin(t))\vec{a} \] 3. (Option): I can only find the general solution for this problem using the Variation of Parameters method. Undetermined Coefficients won't work in this case. 4. (Option): I can find the general solution using the undetermined coefficients method. To find the particular solution I should use a try function of the form \[ \vec{Y}(t) = \sin(t)\vec{a} \]
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