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Stephanie Campbell
Assignment 1
MATH263, Fall 2010
due 09/12/2010 at 11:55pm EDT.
You may attempt any problem an unlimited number of times.
1.
(1 pt) Match each of the following differential equations
with a solution from the list below.
1.
y
00
+
y
=
0
2. 2
x
2
y
00
+
3
xy
0
=
y
3.
y
00

12
y
0
+
32
y
=
0
4.
y
00
+
12
y
0
+
32
y
=
0
A.
y
=
e

8
x
B.
y
=
1
x
C.
y
=
e
4
x
D.
y
=
cos
(
x
)
Correct Answers:
•
D
•
B
•
C
•
A
2.
(1 pt) Match each of the differential equation with its
solution.
1.
y
00
+
13
y
0
+
40
y
=
0
2. 2
x
2
y
00
+
3
xy
0
=
y
3.
xy
0

y
=
x
2
4.
y
00
+
y
=
0
A.
y
=
3
x
+
x
2
B.
y
=
e

8
x
C.
y
=
x
1
2
D.
y
=
sin
(
x
)
Correct Answers:
•
B
•
C
•
A
•
D
3.
(1 pt) Match each differential equation to a function which
is a solution.
FUNCTIONS
A.
y
=
3
x
+
x
2
,
B.
y
=
e

8
x
,
C.
y
=
sin
(
x
)
,
D.
y
=
x
1
2
,
E.
y
=
4exp
(
6
x
)
,
DIFFERENTIAL EQUATIONS
1.
y
00
+
12
y
0
+
32
y
=
0
2.
y
0
=
6
y
3. 2
x
2
y
00
+
3
xy
0
=
y
4.
xy
0

y
=
x
2
Correct Answers:
•
B
•
E
•
D
•
A
4.
(1 pt) Match the following differential equations with their
solutions.
The symbols
A
,
B
,
C
in the solutions stand for arbitrary con
stants.
You must get all of the answers correct to receive credit.
1.
d
2
y
dx
2
+
81
y
=
0
2.
dy
dx
=

2
xy
x
2

9
y
2
3.
d
2
y
dx
2
+
12
dy
dx
+
36
y
=
0
4.
dy
dx
=
18
xy
5.
dy
dx
+
18
x
2
y
=
18
x
2
A.
y
=
Ce

6
x
3
+
1
B. 3
yx
2

9
y
3
=
C
C.
y
=
A
cos
(
9
x
)+
B
sin
(
9
x
)
D.
y
=
Ae
9
x
2
E.
y
=
Ae

6
x
+
Bxe

6
x
Correct Answers:
•
C
•
B
•
E
•
D
•
A
5.
(1 pt) Just as there are simultaneous algebraic equations
(where a pair of numbers have to satisfy a pair of equations)
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