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Chapter 1
0
5
51
0
c
=
−
5
c
=
−
4
c
=
−
3
c
=
−
2
c
=
−
1
c
=1
c
=2
c
=3
c
=4
3
Figure 1–B
: Isoclines and the direction feld For Problem 17.
and so the elements oF the direction feld have
negative
or
zero slope
; iF an isocline is located
below
the line
y
=3
,then
c>
0, and so the elements oF the direction feld have
positive slope
.
In other words, For
x>
0 large enough, at any point above the line
y
= 3 a solution curve
decreases passing through this point, and any solution curve increases passing through a point
below
y
= 3. The direction feld For this di±erential equation is depicted in ²igure 1B. ²rom
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This note was uploaded on 03/29/2010 for the course MATH 54257 taught by Professor Hald,oh during the Spring '10 term at University of California, Berkeley.
 Spring '10
 Hald,OH
 Math, Differential Equations, Linear Algebra, Algebra, Equations, Slope

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