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.pdfSchool
Southern Illinois University, Edwardsville **We aren't endorsed by this school
Course
MATH MATH-305
Subject
Mathematics
Date
Nov 20, 2023
Type
Other
Pages
2
Uploaded by HighnessStar22307 on coursehero.com
Homework
6
Due
7/19/21
MATH
305
Name
k
@,\},
1.
(5)
A
population
follows
the
logistic
equation
4&
=
P
(120
—
3P),
with
P
(0)
=
10.
(a)
Draw
the
phase
portrait.
1.
Find
the
critical
points.
f
(
(20
-
2F>
=0
Pz0
or
Pzt0
2.
Place
the
arrows
of
the
phase
portrait
on
the
P-axis.
3.
Include
the
lines
for
the
critical
points.
4.
Sketch
a
typical
solution curve
that
goes
through
P
(0)
=
10.
P40
<
ho-30
<o
L
Al
=
Fr
<0
T
U
»,fixlgg
o<PcYo=Po0
;
}
C
o
Flee
Lot
f
ho-30
¢
/C%'/Pe,'g::
Pr.
:—:>d/d
AL
20
j
;
:
|
=g
60
-0
40
30
20
-I0
@
0
20
30
40
50
6
P
'
U
P<0
ac-3p
56
(b)
Find
P
(t)
by
using
the
generic
solution
P
(t)
=
m{ff&;@fi
=
ff?
<g)
a<lro
b=3
,
=
(0
o
Fo
p(fijvéfilfiiflfifi
S22
TGy
4
(1re
()0
P(t):
g%?alé;,
1200
-
/aro
=
e
mRe
T
e
s
3o
tgce
3
#9'6"{1'76
(c)
|
Carrying
capacity
=
40
(d)
At
what
time
will
the
population
equal
one-half
the
carrying
capacity?
Show
your
work.
Write
your
answer
in
the
box.
\
_3¢]
PLO=
4
(10)
>
3550w
720
=
Po=20G
7
—
/53'6@"?"{'"36'(}*"9
e
=
b
Dot
=l
(k)
€77
15
.
000
2.
(3)
Given
the
DE
zy"
+
¢/
+
25y
=0
(a)
Let
IVP
be
the
DE
with
the
initial
conditions
y
(2)
=
4
and
%/
(2)
=
6.
Find
the
largest
interval
containing
zo
=
2
such
that
Th.
4.1.1
guarantees
that
the
IVP
has
a
unique
solution.
Show
your
work.
Write
your
answer
in
the
box.
Q
"){*\'E
=
B
%
>
NS
ED?
)L
504%
condimvous
on
(-,
o}
&,
(x
)=
2
(-co
1)
Y
o
comdinudind
o,
AR
.
Go
()=
%=l
or
(10,c0)
=
IVP
has
G
urigle
7
/'(k):'
O
C'Ow-g/mé{w&&
s
-
g
.
v
o
e
wotilion
an
(200)
G
(wy=%Z0
Lf;%av@/af
thepm
Yzp
Interval
=
(
o
{
Cf)
(b)
Let
BVP
be
the
DE
with
the
boundary
conditions
y
(2)
=
4
and
y
(4)
=
8.
1.
Does
Th.
4.1.1
gurantee
the
existence
of
a
solution
on the
interval
you
found
in
Part
(a)?
(circle
one)
Yes
@
Th,
41
|
Hdoes
ot
a/ap//kf
to
/f?é/f?g.
2.
Does
Th.
4.1.1
gurantee
the
uniqueness
of
a
solution
on
the
interval
you
found
in
Part
(a)?
(circle
one)
Yes
@5
3.
(1)
Show
your
work.
The
functions
=2z,
fo(2)
=2+
3,
f3
(x)
=
6z
+
6
are
linearly
(circle
one):
1.
Independent
:
Dependirvio/':}
x4y
(xtz)=
Ex+é
Ly
talxez)-(exte]z0
R\Q(k}';iéfih(k)wr@
(j=o0
Led
C,=2
C,
2
C31'~/
"
3
CLJ
<,
¢
3
G
C\'
(}')
+
o
{;,,(;:;}
Tj'
G
\(;
('%j
=G
&
s
4.
(1)
Show
your
work.
The
functions
f;
(z)
=
2z,
fo
(z)
=z
+
3,
f3(z)
=
2%
+
2
are
linearly
(circle
one):
1.
Independé&d
2.
Dependent
Seppese
Qd
+
e,
£C)
te,
BE(x
=0
g
2w
ta
Gz
GO
)
o
CR
3
A
(2¢
%C},},}fi'f
+
35-)%'1(3
jakzq«éox.&
o
€3
O
;
/
<&
%
!
'
>
A';
AT
E
Ty
2O
—>
G,z
o
.
QJ.[XS
&
e
//if'?é&(r{f)
"'Géf?@?fiwdfff.
ey
2,
420,
70
>
=0
