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MATH 216 FINAL EXAM
April 23, 2010
Please write your name:
4po
ints
Section:
The test contains 8 problems worth 100 points total.
To get the full credit you
have to show your work
.
Page 12 contains a table of useful Laplace transforms.
12
Problem
Points
Score
12
1
2
3
12
4
12
5
12
6
7
12
Total
8
12
12
Typeset by
A
M
S
T
E
X
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View Full Document Name:
(
12 points
)
1. Problem.
Find the solution
x
(
t
)
,y
(
t
)tothesystemo
fd
i±erent
ia
l
equations
x
±
=3
x

2
y
y
±
=4
x

y
satisfying the initial conditions
x
(0) = 1 and
y
Name:
(
12 points
)
2. Problem.
Find all critical points of the system of di±erential
equations for functions
x
(
t
)and
y
(
t
)be
lowanddeterm
inethe
irstab
i
l
ity
x
±
=
xy

3
x
y
±
=
x
+
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View Full Document Name:
(
12 points
)
3. Problem.
Match the systems of diFerential equations for functions
x
(
t
)and
y
(
t
)be
loww
iththe
ird
irect
ion±e
ldsonthenextpage
.
1)
x
±
=
y
y
±
=
x
²igure
2)
x
±
=
x
+2
y
y
±
=

2
x
+
y
²igure
3)
x
±
=

y
y
±
=
x
²igure
4)
x
±
=3
x
+
y
y
±
=
x
+3
y
²igure
5)
x
±
=

x
+2
y
y
±
=

2
x

y
²igure
6)
x
±
=

3
x
+
y
y
±
=
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This note was uploaded on 01/30/2012 for the course MATH 216 taught by Professor Stenstones? during the Fall '07 term at University of Michigan.
 Fall '07
 Stenstones?
 Math

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