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Name:
SID:
Section:
Instructor:
EXAM I
MATH 251
October 14, 2003
•
This is a closed book exam. No notes or calculators may be
used.
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9
10
Total:
1
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(1) (8 points) For each of the di±erential equations below, state its order and whether
it is linear or nonlinear.
(a)
y
0
+
t
2
y
=
e
t
(b) 2
y
00
+ 3
y
0

y
=
te

t
(c)
y
0
=
y
(
y
+ 1)(
y

1)
(d)
y
000

2
y
0
+
ty

y
2
= 0
(2) (5 points) The integrating factor used to solve 2
t
2
y
0
+ 6
ty
=
e

3
t
is
(a)
e
3
t
(b)
e
3
t
2
(c)
t
3
(d)
e

3
t
3
(3) (5 points) The Existence and Uniqueness Theorem guarantees that the solution
to
sin(
t
)
y
00
+
1
t

3
y
0
+
e
t
y
=
t
3
,
y
(1) = 0
,
y
0
(1) = 1
is valid on
(a) (0
,
3)
(b) (0
, π
)
(c) (
∞
,
3)
(d) (
∞
,
∞
)
(4) (5 points) Which of the following is the general solution of
y
00
+ 9
y
= 0?
(a)
c
1
e
3
t
+
c
2
e

3
t
(b)
c
1
e

3
t
+
c
2
te

3
t
(c)
c
1
e

9
t
+
c
2
(d)
c
1
cos 3
t
+
c
2
sin 3
t
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(5) (12 points) Solve the initial value problem
y
0
=
4
x
3

6
x
+ 3
2
y
+ 8
,
y
(1) =

2
.
Give your answer in explicit form.
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This note was uploaded on 07/23/2008 for the course MATH 251 taught by Professor Chezhongyuan during the Spring '08 term at Pennsylvania State University, University Park.
 Spring '08
 CHEZHONGYUAN
 Differential Equations, Equations, Partial Differential Equations

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