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?
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?
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 12CR
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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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