This preview shows page 1. Sign up to view the full content.
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
00

xy
0
+
y
=
0
,
y
(
0
) =

2
,
y
0
(
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
00

y
0
+
6
y
=
0
,
y
(
0
) =
0
,
y
0
(
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
00

(
sin
x
)
y
=
cos
x
,
y
(
0
) =
3
,
y
0
(
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
00
+
3
(
x

1
)
y
0

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
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 12/01/2010 for the course MATH 263 taught by Professor Sidneytrudeau during the Fall '09 term at McGill.
 Fall '09
 SidneyTrudeau
 Math

Click to edit the document details