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7/27/2019 ODE E Assignment3
1/7
ODE E3 - 1
ODE Chapter 3 EAssignment
Approximate Solution on Direction Fields
3-1 (ODE Nov 1999 Q6) The solution curve of the initial value problem
1)0(,2
1)sin( =+= yyxxy
dx
dy
goes through precisely one of the five pointsA, .,Eindicated below on the
direction field for the differential equation. Determine that point.
E
D
C
B
A
(E)
(D)
(C)
(B)
(A)
7/27/2019 ODE E Assignment3
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ODE E3 - 2
3-2 (ODE Jun 2000 Q5) The solution curve of the initial value problem
1)0(,2
1)sin( =+= yyxxy
dx
dy
goes through precisely one of the five pointsA, .,Eindicated below on thedirection field for the differential equation. Determine that point.
E
D
CB
A
(E)
(D)
(C)(B)
(A)
7/27/2019 ODE E Assignment3
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ODE E3 - 3
3-3 (ODE Oct 2002 Q6) The diagram below represents the direction field of
2
1(E)
1
2(D)
1
2(C)
2
1(B)
21(A)
+
+
+
+
x
y
x
y
x
y
x
y
xy
7/27/2019 ODE E Assignment3
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ODE E3 - 4
Long Term Behavior of Differential Equations
3-4 (ODE Nov 1999 Q7) It is known that the behavior asxincreases fromx0= 0 of the
solutiony(x) of the differential equation ),( yxfy = , whose direction field is below,
satisfying 0)0( yy = , depends only on the value of 0y .
+>
==
7/27/2019 ODE E Assignment3
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ODE E3 - 5
3-5 (ODE Jun 2000 Q6) It is known that the behavior asxincreases fromx0= 0 of the
solutiony(x) of the differential equation ),( yxfy = , whose direction field is below,
satisfying 0)0( yy = , depends only on the value of 0y .
==
xas1)(then,51If(E)1)(then,1If(D)
as0)(then,1If(C)
as)(then,5If(B)
5)(then,5If(A)
0
0
0
0
0
xyyxyy
xxyy
xxyy
xyy
3-6 (ODE Jun 2000 Q13) A population P satisfies the initial value problem
1000)0(),500(20 == PPPdt
dP
Then Pwill
decreasethenfirstatincrease(E)
increasethenfirstatdecrease(D)
towardstendandtallforincrease(C)
valuelimitingaapproachandtallfordecrease(B)
valuelimitingaapproachandtallforincrease(A)
7/27/2019 ODE E Assignment3
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ODE E3 - 6
3-7 (ODE Undated Q7) The behavior of the solutiony(x) of the differential equation
)1)(2( yyy += satisfying 0)0( yy = depends only on the value of 0y . Which of
the following is NOT true
7/27/2019 ODE E Assignment3
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ODE E3 - 7
3-10 (ODE Aug 2006 Q4) For the autonomous DE
=
2sin)1( y
yedx
dy y , indicate the
constant solutions and the regions of positive and negative slope on a direction field
to determine how many of the following statements are true
=
=
=
=
xasxfthenfif
xasxfthenfif
xallforxfthenfif
xasxfthenfif
)(0)0(
2)()0(
1)(1)0(
1)()0(
21
21
.4(E)
.3(D)
.2(C)
.1(B)
.0(A)
3-11 (ODE Mar 2007 Q4) For the autonomous DE
=
2sin)1( y
yedx
dy y , indicate
the constant solutions and the regions of positive and negative slope on a directionfield to determine how many of the following statements are true
=
=
=
=
xasxfthenfif
xasxfthenfif
xallforxfthenfif
xasxfthenfif
)(0)0(
2)()0(
1)(1)0(
1)()0(
21
21
.4(E)
.3(D)
.2(C)
.1(B)
.0(A)