MATH 251
Examination I
July 8, 2008
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This exam has 11 questions for a total of 100 points.
In order to obtain full credit for partial
credit problems, all work must be shown. Credit will not be given for an answer not
supported by work.
The point value for each question is in parentheses to the right of the
question number.
You may not use a calculator on this exam. Please turn off and put away your
cell phone.
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2:
3:
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11:
Total:
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EXAMINATION I
July 8, 2008
1. (5 points) Which of the following ﬁrst order diﬀerential equation is
both
linear and au
tonomous?
(a)
y
0
+
ty
= 0
(b)
y
0

y
3
= 2
(c)
y
0
+ 4
y
=
π
(d)
y
0
+
e
y

5
t
= 0
2. (5 points) Consider the initial value problem
(
t
2

16)
y
0
+ sin(
t
5
)
y
=
t
+ 1
t

1
,
y
(
π
) =
1
2
.
Without solving the equation, what is the largest interval in which a unique solution is guar
anteed to exist?
(a) (1
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 Spring '08
 CHEZHONGYUAN
 Math, Differential Equations, Equations, Partial Differential Equations, Litre, Boundary value problem

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