;":ji:il:f:tr::i;
ji::::.::4.'::::ti
In each of.Problems 1 through 6 draw a direction field for the given
'ROBLEMS
differential equation.
::1:lr::j:i'::::j:::'::r"'::rji'd:::+
Based on the direc{ion fierd, determine the behavior of y as r -+ oo. If
this behavior depends
on the initial value€fy at I : 0, describe the dependency.
efi r'Y':3-2Y
d ? 2.y' :2y- 3
&l_J. 3. y' :3 + 2y
{#;1, 5.y':r+2y
;{L
d{"
4. y, : -r - 2y
6.y,:y*2
Ineachof ProblemsTthroughl0writedownadifferential equationof theformdy/dt:
whose solutions have the required behavior as / -+ oo.
7. Alls o l u t i o n s a p p r o a c h y : 3 .
ay* b
8 . A l l s o l u t i o n s a p p r o a c h y :2 /3 .
9. AII other solutions diverge from y : ).
10. All otherfolutions diverge from y : l/f .
In each of Problems 11 through l4 draw a direction field for the given dift'erential equation.
Based on the direction field, determine the behavior of y as / --+ oo. If this behavior depends
on the initial value of y at t:O,describe this dependency.Note that in these problems the
equations are not of the form l' : uy * b, and the behavior of their solutions is somewhat
more complicated than for the equations in the text.
62
&
11..y' : y(4 - y)
L r.y -y '
6,L tz y' : -y(s - y)
62 u y' : y(y -2)2
consider the following list of differential equations, some of which produced the
A^lI-
^ L ^ . . , ..:..
n :- - - - - - -
|
r
- .r