Exam 1 Review
MAP 2302
Disclaimer:
This review is by no means complete.
Please study the homework as well as the lecture
notes. These questions are just an outline of the material.
1. Chapter 1 KNOW: definition of differential equation, difference between explicit and implicit so
lution, initial value conditions, how to sketch a graph, isocline, given a direction field sketch the
approximate solution.
(a) Solve
dy
dx
= ln(
x
) with
P
= (1
,
1).
(b) Let
dy
dx
=
r
2
π
sin(
x
2
). Where is the solution monotonic? What symmetry (if any) does
y
(
x
)
have?
2. Chapter 2 KNOW: autonomous first order differential equation, equilibrium solutions, stable, unsta
ble and semistable solutions, phase line, ExistenceUniqueness theorem, applications like Malthus
Models (simple exponential growth), and Logistic Models.
(a) Determine the behavior of the equilibria for
dy
dx
=
y
(
y

1)
2
.
(b) Let
dy
dx
=
y
1
/
3
through the point (0
,
0). What does the ExistenceUniqueness theorem state?
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 Summer '08
 TUNCER
 Numerical Analysis, dy, Logistic function

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