Math 3301
Homework Set 1
10 Points
Sketch the direction field for each of the following differential equations.
Based on your direction field
sketch determine the behavior of the solution,
Basics
( )
yt
, as
t
→∞
(
i.e.
the long term behavior).
If this
behavior depends upon the value of
( )
0
y
give this dependence.
1.
( ) ( )( )
2
42
2
4
dy
y
yy
dt
=
+
−−
2.
( )( )
3
22
1
y
−
′
=
−+
e
For problems 3 & 4 solve the given IVP.
Linear Differential Equations
3.
( ) ( ) ( )
2
2
23
2
2
2
04
x
x
y
xy
x
y
−
′
+
=
++
=
e
4.
( ) ( )
4
4
3
76
3
2
3
10
t
ty
t
t y t
y
′
− +
=
−=
e
5.
It is known that the solution to the following differential equation will have a relative maximum at
1
2
t
=
.
Assuming that the solution and its derivative exist and are continuous for all
t
determine the
value of the solution at this point (
i.e.
find
( )
1
2
y
).
Note that because you don’t have an initial condition
you can’t actually solve this differential equation.
It is still possible however to answer this question.
6
43
t
′
+=
−
e
Hint : Recall from Calc I where relative extrema may occur and don’t forget the differential equation,
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This note was uploaded on 03/13/2009 for the course MATH 2171 taught by Professor Deng during the Spring '08 term at UNC Charlotte.
 Spring '08
 Deng
 Differential Equations, Equations

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