2 Series Solutions to Linear Ordinary Differential Equations II
Examples: Solutions about an Ordinary Point
(
29
(
29 (
29
(
29 (
29
⋅
⋅
⋅

⋅
⋅
+
⋅

+
⋅
⋅
⋅

⋅
⋅
+
⋅

=
7
4
1
6
3
0
x
3
4
6
7
1
x
3
4
1
x
c
x
2
3
5
6
1
x
2
3
1
1
c
x
y
This gives two solutions
(
29
(
29 (
29
(
29 (
29 (
29
⋅
⋅
⋅
+
⋅
⋅
⋅

⋅
⋅
+
⋅

=
9
6
3
1
x
2
3
5
6
8
9
1
x
2
3
5
6
1
x
2
3
1
1
x
y
(
29
(
29 (
29
(
29 (
29 (
29
⋅
⋅
⋅
+
⋅
⋅
⋅

⋅
⋅
+
⋅

=
10
7
4
2
x
3
4
6
7
9
10
1
x
3
4
6
7
1
x
3
4
1
x
x
y
Note:
(
29
(
29 (
29
(
29 (
29 (
29
⋅
⋅
⋅
+
⋅
⋅
⋅

⋅
⋅
+
⋅

=
9
6
3
1
x
2
3
5
6
8
9
1
x
2
3
5
6
1
x
2
3
1
1
x
y
(
29
(
29
(
29
(
29
(
29
(
29
(
29
(
29
(
29
⋅
⋅
⋅
+




+



+


+
=
9
9
6
6
3
3
x
1
3
3
1
6
6
1
9
9
1
1
1
6
6
1
3
3
x
1
3
1
3
x
1
1
(
29
(
29
(
29
(
29
(
29
(
29
(
29
(
29
(
29
⋅
⋅
⋅
+




+



+


+
=
⋅
⋅
⋅
3
3
9
2
3
6
1
3
3
x
1
3
3
1
6
6
1
9
9
1
1
1
6
6
1
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 Fall '08
 Prinja
 ORDINARY DIFFERENTIAL EQUATIONS, ordinary point, Linear Ordinary Differential Equations II

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