MATH 3103
Fall 2011
Diﬀerential Equations
Homework Set 2
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 #
10
:
*
Section 1.1 #
26
:
[If sketching the direction ﬁeld by hand, one can begin by using the
isoclines
, curves on which
y
0
is
constant. In this case, we have
y
0
=

2 +
t

y
, so
y
0
=
c
when

2 +
t

y
=
c
, or
y
=
t

(2 +
c
);
that is, all points on each straight line of slope
dy/dt
= 1 have the same value of
y
0
in the direction
ﬁeld. Hence we have, for instance,
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 Spring '11
 RWK
 Math, Differential Equations, Equations, order differential equation

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