MAP 2302 — PRACTICE MIDTERM EXAM — SPRING 2011
NAME
GROUP NUMBER
Instructions: All work should be written in a proper and coherent manner. Write in such a
way that any student in the class can follow your work. When working problems show all
your work. Answers with no work or explanations will receive no credit, unless otherwise
specified. Each member of a team must submit the solution of a different problem.
Do only SIX problems. If you do more than six problems, then the best 6 problems are
counted.
TOTAL POSSIBLE
: 60 points.
(1) [
10 points
] Determine whether the Existence Uniqueness Theorem implies that the
Initial Value Problem
dy
dx
=
1
x

√
y

1
,
y
(2) = 1
,
has a unique solution on some interval containing
x
= 2.
(2) [8 + 2 = 10
points
] (i) Solve the Initial Value Problem
dy
dx
=
x
+ 2
y,
y
(0) = 0
.
(ii) Below is the direction field plot for the differential equation
dy
dx
=
x
+ 2
y.
–2
–1
0
1
2
y(x)
–2
–1
1
2
x
Plot the solution to the initial value problem (in (i)) on this direction field plot.
(3) [
10 points
] Solve the following initial value problem. Your solution
y
should be given
explicitly in terms of
x
.
dy
dx
+
y
3
e
sin
x
cos
x
= 0
,
y
(0) = 1
.
1
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 Spring '08
 TUNCER
 Boundary value problem, coherent

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