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Unformatted text preview: NAME : MAP 2302 — Elementary Diﬀerential Equations — Fall 2011
September 12, 2011
Midterm 1 Instructions: This is a closed book exam and no notes are allowed. You are not to provide or
receive help from any outside source during the exam except that you may ask the instructor for
clariﬁcation of a problem. You have 50 minutes and you should attempt all problems.
• Print your name in the space provided.
• Sign the FERPA release on the next page only if you wish your exam returned in lecture.
• Calculators or other computing devices are not allowed.
• Except when indicated, you must show all work and give a reason (or reasons) for your
answer. A correct answer with incorrect work will be considered wrong. FERPA Release: Because of privacy concerns, I will not return your graded exams in lecture
without your permission. If you want me to return your exam in lecture, please sign on the line
indicated below. Otherwise, you may collect your exam during my oﬃce hours.
SIGN HERE: . Problem Points 1 25 2 25 3 25 4 25 Total 100 Score 1. (25) Indicate whether each of the following diﬀerential equations are separable or linear.
Indicate the integrating factor for the linear diﬀerential equations. Do not attempt to solve
these equations. You do not need to show any work.
a. dy
= 2xy sin(x + y ).
dx
Separable? No Linear?
b. Yes
Yes No If yes, integrating factor: dy
= 2y sin x − cos x.
dx
Separable? No If yes, integrating factor: Yes No Linear? Yes No If yes, integrating factor: Separable? Yes No Linear?
e. Yes Separable? d. No Linear?
c. Yes Yes No If yes, integrating factor: Separable? Yes No Linear? Yes No If yes, integrating factor: x2 − y
dy
=√.
dx
x dy
= xy sin x.
dx x3 ln y
dy
=
.
dx
y2 1 2. (25) Solve the diﬀerential equation
dy
cos y + 2xy
=
.
dx
x sin y − x2 2 3. (25) Make an appropriate substitution in order to solve the diﬀerential equation
dy
y
= + ex y 2 .
dx
x 3 4. (25) Solve the initial value problem
1
y (0) = .
e dy
xy
=
;
dx
ln y 4 5 ...
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 Fall '08
 TUNCER
 Elementary algebra, Boundary value problem, A Closed Book, dy, FERPA

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