or the system of differential equations, y² = [ 28 23 84 -6 - 22 O Find the characteristic polynomial of the matrix of coefficients A. CA(X): A1, A2 = ) Find the eigenvalues of A. Enter the eigenvalues as a list in ascending order eparated by commas. 21 3 4et y + Find the eigenvectors assuming u₁ is the eigenvector associated with the smaller igenvalue A₁ and u₂ is the eigenvector associated with the larger eigenvalue A₂. Enter ne eigenvectors as a matrix with an appropriate size. = U₂ =
or the system of differential equations, y² = [ 28 23 84 -6 - 22 O Find the characteristic polynomial of the matrix of coefficients A. CA(X): A1, A2 = ) Find the eigenvalues of A. Enter the eigenvalues as a list in ascending order eparated by commas. 21 3 4et y + Find the eigenvectors assuming u₁ is the eigenvector associated with the smaller igenvalue A₁ and u₂ is the eigenvector associated with the larger eigenvalue A₂. Enter ne eigenvectors as a matrix with an appropriate size. = U₂ =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Transcribed Image Text:For the system of differential equations,
3
23 84
6 - 22
4et
a) Find the characteristic polynomial of the matrix of coefficients A.
CA(X)
A1, A2
b) Find the eigenvalues of A. Enter the eigenvalues as a list in ascending order
separated by commas.
U₁ =
U₂ =
c) Find the eigenvectors assuming u₁ is the eigenvector associated with the smaller
eigenvalue X₁ and u₂ is the eigenvector associated with the larger eigenvalue λ₂. Enter
the eigenvectors as a matrix with an appropriate size.
y'
=
v(t)
y +
d) Determine a general solution to the system by completing the following steps.
i. Find v(t) = [Y-¹(t)f(t)dt .
ii. Find a particular solution y(t).
H
yp(t)=
y(t)
ii. Then a general solution for the system in the matrix form is
-8:33:
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Follow-up Question
![For the system of differential equations,
v(t) =
ii. Find a particular solution y(t).
Determine a general solution to the system by completing the following steps.
i. Find v(t) = fx-¹(t)f(t)}dt .
y₂(t)=
y' =
ii. Then a general solution for the system in the matrix form is
18.1281:
y(t) =
23
84
22 ] Y + [ ₁ ² ]
y
4et
-6-22.](https://content.bartleby.com/qna-images/question/2323f944-68c6-4ffb-b4bd-7709a3866c17/60c8d54e-4f25-46bf-a92f-5793f15ae9ab/tjjevie_processed.png)
Transcribed Image Text:For the system of differential equations,
v(t) =
ii. Find a particular solution y(t).
Determine a general solution to the system by completing the following steps.
i. Find v(t) = fx-¹(t)f(t)}dt .
y₂(t)=
y' =
ii. Then a general solution for the system in the matrix form is
18.1281:
y(t) =
23
84
22 ] Y + [ ₁ ² ]
y
4et
-6-22.
Solution
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