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Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Please answer problem d
![nnal soluttion in
förm, then verify directly that your solution solves the IVP.
Problem 2. Consider the system of linear differential equations for two real valued functions
and y(t):
Sx'(t) = -3x(t) – y(t)
ly'(t) = x(t) – y(t)
(a) Write the above system in matrix form X'(t) = AX (t), where X (t) =
(b) Solve your system from part (a) to find two linearly independent vector solutions, i(t) and
42(t).
(c) Directly demonstrate that these two vector solutions e1(t) and 42(t) are linearly indepen-
dent (hint: examine the Wronskian determinant).
(d) Considering the initial conditions x(0) = 5 and y(0) = 2, find the particular soluțion to the
system of ODES in vector form, and then clearly state the component solutions x(t] and Y (t).
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(e) Plot x(t) and y (t) on the same axis
determine their end behaviors.
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B.](https://content.bartleby.com/qna-images/question/1dfec151-558e-4c66-9085-1fd1afee3454/6a258fb2-59ee-4671-b00d-f3289251c3ca/k3lxxeus_thumbnail.jpeg)
Transcribed Image Text:nnal soluttion in
förm, then verify directly that your solution solves the IVP.
Problem 2. Consider the system of linear differential equations for two real valued functions
and y(t):
Sx'(t) = -3x(t) – y(t)
ly'(t) = x(t) – y(t)
(a) Write the above system in matrix form X'(t) = AX (t), where X (t) =
(b) Solve your system from part (a) to find two linearly independent vector solutions, i(t) and
42(t).
(c) Directly demonstrate that these two vector solutions e1(t) and 42(t) are linearly indepen-
dent (hint: examine the Wronskian determinant).
(d) Considering the initial conditions x(0) = 5 and y(0) = 2, find the particular soluțion to the
system of ODES in vector form, and then clearly state the component solutions x(t] and Y (t).
Access more tools and enhanced fu
(e) Plot x(t) and y (t) on the same axis
determine their end behaviors.
P Type here to search
ASUS ZenBook
esc
no
insert
3
4.
8.
9
tob
E
Y
U
P
caps lock
A
S
G
H
shiftO
V
fn
alt
alt
ctrl
B.
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