In Exercises 1-4, each of the linear systems has one eigenvalue and one line of eigen- vectors. For each system, (a) find the eigenvalue; (b) find an eigenvector; (e) sketch the direction field; (d) sketch the phase portrait, including the solution curve with initial condition Yo = (1,0); and (e) sketch the x(t)- and y(t)-graphs of the solution with initial condition Yo = (1,0). dY dt -3 -(19) -3 dY dt - (11)x 22-(-31)x = 2. dY dt 4. d dt = - (-1-2) Y
In Exercises 1-4, each of the linear systems has one eigenvalue and one line of eigen- vectors. For each system, (a) find the eigenvalue; (b) find an eigenvector; (e) sketch the direction field; (d) sketch the phase portrait, including the solution curve with initial condition Yo = (1,0); and (e) sketch the x(t)- and y(t)-graphs of the solution with initial condition Yo = (1,0). dY dt -3 -(19) -3 dY dt - (11)x 22-(-31)x = 2. dY dt 4. d dt = - (-1-2) Y
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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HELP !!! 1 & 3 Please !
Transcribed Image Text:In Exercises 1-4, each of the linear systems has one eigenvalue and one line of eigen-
vectors. For each system,
(a) find the eigenvalue;
(b) find an eigenvector;
(c) sketch the direction field;
(d) sketch the phase portrait, including the solution curve with initial condition
Yo = (1, 0); and
(e) sketch the x(t)- and y(t)-graphs of the solution with initial condition Yo = (1, 0).
1.
3.
dY
dt
dY
dt
-3 0
=
- ( 1_ ) x
1-3
-2 -1
1 -4
Y
2.
4.
dY
dt
dY
dt
=
(
2
-1
1
4)
Y
0
-1 -2
1
(2) ₁
Y
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