MATH 3103
Fall 2011
Diﬀerential Equations
Homework Set 1
Some Solutions
The following solutions are not necessarily complete, but should highlight the main points for most
questions. If you have any further questions regarding the problems and solutions, feel free to discuss
them on WebCT.
Solutions marked by
*
are taken from the publisher’s Instructor’s Solutions Manual for the textbook by
Boyce and DiPrima, 9th edition (Wiley), while solutions marked by
†
(which appear to have been typed
with a typewriter.
. . ) are from the publisher’s Student Solutions Manual; in some cases I have added
comments in [brackets].
Section 1.1:
*
Section 1.1 #
3
:
[More correctly, the solution should say that all
other
solutions diverge from the (unstable) equi
librium solution
y
(
t
)
≡ 
3
/
2.]
†
Section 1.1 #
11
:
[The steady state
y
= 0 is unstable, while
y
= 4 is stable. The resulting direction ﬁeld, produced
using Maple, is given below:]
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Section 1.1 #
15–20
:
These problems ask one to identify the diﬀerential equations producing the given direction ﬁelds.
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 Spring '11
 RWK
 Math, Differential Equations, Thermodynamics, Equilibrium, Equations, Steady State, Stability theory, Attractor

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