Stephanie Campbell
Assignment 7
MATH263, Fall 2010
due 12/01/2010 at 11:55pm EST.
You may attempt any problem an unlimited number of times.
1.
(1 pt) Find the indicated coefficients of the power series
solution about
x
=
0 of the differential equation
(
x
2
+
4
)
y

xy
+
y
=
0
,
y
(
0
) =

2
,
y
(
0
) =

3
y
=

2

3
x
+
x
2
+
x
4
+
x
6
+
x
8
+
O
(
x
9
)
2.
(1 pt) Find the indicated coefficients of the power series
solution about
x
=
0 of the differential equation
(
x
2

x
+
1
)
y

y
+
6
y
=
0
,
y
(
0
) =
0
,
y
(
0
) =
7
y
=
7
x
+
x
2
+
x
3
+
x
4
+
x
5
+
O
(
x
6
)
3.
(1 pt) Find the indicated coefficients of the power series
solution about
x
=
0 of the differential equation
y

(
sin
x
)
y
=
cos
x
,
y
(
0
) =
3
,
y
(
0
) =
8
y
=
3
+
8
x
+
x
2
+
x
3
+
x
4
+
O
(
x
5
)
4.
(1 pt) Consider the differential equation
2
x
(
x

1
)
y
+
3
(
x

1
)
y

y
=
0
which has a regular singular point at
x
=
0. The indicial equa
tion for
x
=
0 is
r
2
+
r
+
=
0
with roots (in increasing order)
r
1
=
and
r
2
=
Find the indicated terms of the following series solutions of
the differential equation:
(a)
y
=
x
r
1
(
5
+
x
+
x
2
+
x
3
+
x
4
+
...
)
(b)
y
=
x
r
2
(
4
+
x
+
x
2
+
x
3
+
x
4
+
...
)
The closed form of solution (a) is
y
=
5.
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 Fall '09
 SidneyTrudeau
 Math, Taylor Series, Stephanie Campbell

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