5. Consider two general solutions of two different linear systems of equations X'(t) = AX(t): A. X(t)=c₁e B. X(t)=c₁e -2 -4 -t [2] The phase portraits for these solutions are below: -2 [2] 0 2 -4t -4t + c₂e XX 4 -2 + c₂e -t ] 0 2 4 Which phase portrait corresponds to general solution A? To B? How do you know?

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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5.
Consider two general solutions of two different linear systems
of equations X'(t) = AX(t):
A. X(t) = c₁e
4
2
0
-2
-4t
-2
B. X(t) = c₁e
The phase portraits for these solutions are below:
XX
0 2 4
2
-4
+ c₂e
-2
4t
-t
+ c₂e-
0
H
2
4
Which phase portrait corresponds to general solution A? To B? How do
you know?
Transcribed Image Text:5. Consider two general solutions of two different linear systems of equations X'(t) = AX(t): A. X(t) = c₁e 4 2 0 -2 -4t -2 B. X(t) = c₁e The phase portraits for these solutions are below: XX 0 2 4 2 -4 + c₂e -2 4t -t + c₂e- 0 H 2 4 Which phase portrait corresponds to general solution A? To B? How do you know?
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