Find two power series solutions of the given differential equation about the ordinary point x = 0. (x - 1)y"+y' = 0 OY₁ = 1 and Y₂ = x + +2²+ + ²³². + +*+ 0₁-1-2+3x4-56+... 8 = 5x6 3x ₁=1+²+¹+²+.. and 2 8 Oy₁ = 1 and Y₂ = x Oy₁ = 1 and Y₂ = x- 16 and y₂ = x - - 2x³ + 8x5 15 +² +3 ₁=x+4 2 3 and y₂ = x + ܀ 3 16x7 35 + 27²8²16x²+.. 35
Find two power series solutions of the given differential equation about the ordinary point x = 0. (x - 1)y"+y' = 0 OY₁ = 1 and Y₂ = x + +2²+ + ²³². + +*+ 0₁-1-2+3x4-56+... 8 = 5x6 3x ₁=1+²+¹+²+.. and 2 8 Oy₁ = 1 and Y₂ = x Oy₁ = 1 and Y₂ = x- 16 and y₂ = x - - 2x³ + 8x5 15 +² +3 ₁=x+4 2 3 and y₂ = x + ܀ 3 16x7 35 + 27²8²16x²+.. 35
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.
(x - 1)y"+y' = 0
OY₁ = 1 and Y₂ = x +
-22²2-
Oy₁ = 1 -
+
Oy₁ = 1 +
3x4
8
+
++2²2324
2
8
Oy₁ = 1 and Y₂ = x
3x
+2²+ + ²³².
+
+*+
I
=
+
5x6
16
5x6
16
+...
+...
- 2x³ + 8x5
3
15
8x5
15
and y₂ = x -
+3
0x₁-1 and Y₂-x-+-+
=
2
3
+2+³55 +
3
and y₂ = x +
+
16x7
35
16x7
35
+
+...
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