Math 322
Assignment 16, Spring 2013
Due at 3 PM Friday May 10th
1. For each of the following systems, draw a phase portrait illustrating the behavior of the solutions,
using the phase
plane plotter that can be found at the class web page
. Be sure to
•
include any trajectories along eigenvectors, which you may just have to put in “by hand”
•
include enough trajectories to give a good idea what is going on in all parts of the phase plane
•
put an arrowhead or two on each trajectory to indicate direction as tie increases
In each case, try to predict what the phase portrait will look like before ±nding it.
(a)
x
′
=
b
−
2
−
2
−
1
2
−
2
B
x
λ
=
−
3
,
−
1,
k
=
b
2
1
B
,
b
−
2
1
B
x
=
c
1
b
2
1
B
e
−
3
t
+
c
2
b
−
2
1
B
e
−
t
(b)
x
′
=
b
2
2
1
2
2
B
x
λ
= 3
,
1,
k
=
b
2
1
B
,
b
−
2
1
B
x
=
c
1
b
2
1
B
e
3
t
+
c
2
b
−
2
1
B
e
t
(c)
x
′
=
b
1
2
3
2
B
x
λ
= 4
,
−
1,
k
=
b
2
3
B
,
b
−
1
1
B
x
=
c
1
b
2
3
B
e
4
t
+
c
2
b
−
1
1
B
e
−
t
(d)
x
′
=
b
3
0
0
3
B
x
λ
= 3,
k
=
b
2
1
B
,
b
−
2
1
B
x
=
c
1
b
2
1
B
e
3
t
+
c
2
b
−
2
1
B
e
3
t
(e)
x
′
=
b
2
−
1
1
4
B
x
λ
= 3,
k
=
b
−
1
1
B
x
=
c
1
b
−
1
1
B
e
3
t
+
c
2
±b
−
1
1
B
te
3
t
+
b
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 Spring '13
 GreggWaterman
 Math, Differential Equations, Equations, Trajectory, λ, −2, e3t + c2

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