Find two power series solutions of the given differential equation about the ordinary point x = 0. y" + x²y = 0 1 1 12 672 Oy=1-- + Oy=1- 1 4 Oy = 1 + x + 6 1 6 1 O y = 1 + Oy=1-²/ + 4 1 252 + 1 252 + 672 -X 1 252 4 8 1 8 8 8 +... -X +... -X and y = x - and y = x - and y = x + 1 20 1 12 and y = x + 3 5 + + 1 5 20 5 1 9 12²³ +672 + -X 1 1440 + and y = x - x² + 12 1 5 -X 672 1 1440 1 672 9 +... 9 -X² -
Find two power series solutions of the given differential equation about the ordinary point x = 0. y" + x²y = 0 1 1 12 672 Oy=1-- + Oy=1- 1 4 Oy = 1 + x + 6 1 6 1 O y = 1 + Oy=1-²/ + 4 1 252 + 1 252 + 672 -X 1 252 4 8 1 8 8 8 +... -X +... -X and y = x - and y = x - and y = x + 1 20 1 12 and y = x + 3 5 + + 1 5 20 5 1 9 12²³ +672 + -X 1 1440 + and y = x - x² + 12 1 5 -X 672 1 1440 1 672 9 +... 9 -X² -
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Find two power series solutions of the given differential equation about the ordinary point x = 0.
y" + x²y = 0
1
12
1
Oy=1-- +
Oy=1- +
1 4
Oy = 1 + x +
6
1
4
O y = 1 +
Oy=1-1x²+
+
1
672
1
252
+
1
252
672
4
252
8
8
1 8
1 8
-X
+...
-X +...
and y = x -
and y = x -
and y = x +
1
20
1
12
and y = x +
3
5
+
+
1 5
20
5 1 9
12²³ +672 +
-X
1
1440
+
and y = x ² +
12
1 5
-X
672
1
1440
1
672
9
+...
9
-X² -
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