Show all your work.The system of three linear DE can be written in the form ZOOM+dYAY where A is a matrix with the following eigenvalues and their associated eigenvectors:dt()()31-5, V1A2 = 3+2 i, V2 =13 = 3 – 2 i, V3 =1x(t)y(t)z(t)and Y(t)is the unknown vector function(i) Find the general real-valued solution of the system(ii) Use (i) to determine if the origin is a source, or a sink, or a saddle

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dY AY where A is a matrix with the following eigenvalues and their associated eigenvectors: dt (E) 3 1 d1 = -5, V1 = d2 = 3+2i, V2 = A3 = 3 – 2i, V3 1 1 x(t) y(t) z(t) ()- and Y(t) = is the unknown vector function (i) Find the general real-valued solution of the system (ii) Use (i) to determine if the origin is a source, or a sink, or a saddle

dY AY where A is a matrix with the following eigenvalues and their associated eigenvectors: dt (E) 3 1 d1 = -5, V1 = d2 = 3+2i, V2 = A3 = 3 – 2i, V3 1 1 x(t) y(t) z(t) ()- and Y(t) = is the unknown vector function (i) Find the general real-valued solution of the system (ii) Use (i) to determine if the origin is a source, or a sink, or a saddle

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

Show all your work.The system of three linear DE can be written in the form

ZOOM
+
dY
AY where A is a matrix with the following eigenvalues and their associated eigenvectors:
dt
()
()
3
1
-5, V1
A2 = 3+2 i, V2 =
13 = 3 – 2 i, V3 =
1
x(t)
y(t)
z(t)
and Y(t)
is the unknown vector function
(i) Find the general real-valued solution of the system
(ii) Use (i) to determine if the origin is a source, or a sink, or a saddle

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