Stephanie Campbell
Assignment 2
MATH263, Fall 2010
due 09/18/2010 at 11:55pm EDT.
You may attempt any problem an unlimited number of times.
1.
(1 pt) Suppose that the initial value problem
y
=
9
x
2
+
5
y
2

7
,
y
(
0
) =
2
has a solution in an interval about
x
=
0.
Find
y
(
0
)
=
.
Find
y
(
0
)
=
.
Find
y
(
0
)
=
.
Note that for
y
(
0
)
and
y
(
0
)
you will have to differentiate the
equation twice (remembering that
y
is a function of
x
) and back
substitute the values given or already calculated.
The Taylor polynomial of degree 3 of the solution about
x
=
0
is
(
T
3
y
)(
x
)
=
.
2.
(1 pt) Find the function
y
=
y
(
x
)
(for
x
>
0 ) which satis
fies the differential equation
x
dy
dx

7
y
=
x
9
,
(
x
>
0
)
with the initial condition:
y
(
1
) =
10
y
=
3.
(1 pt) Solve the initial value problem
dy
dx

10tan
(
5
x
)
y
+
3sin
(
2
x
) =
0
,
y
(
0
) =

4
.
The solution is
y
(
x
) =
4.
(1 pt) Find
u
from the differential equation and initial
condition.
du
dt
=
e

3
t

u
,
u
(
0
) =
6
.
u
=
5.
(1 pt) Find the function
y
=
y
(
x
)
(for
x
>
0 ) which satis
fies the differential equation
dy
dx
=
9
+
16
x
xy
2
,
(
x
>
0
)
with the initial condition:
y
(
1
) =
5
y
=
6.
(1 pt) Consider the differential equation
y
=
1
36
x
(
81

y
2
)
This equation has the 2 constant solutions (in increasing or
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 Fall '09
 SidneyTrudeau
 Math, Constant of integration, Boundary value problem

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