Find two power series solutions of the given differential equation about the ordinary point x = 0. y" 5xy' + y = 0 + x² + 11x4 + 77x6 2 24 240 Oy₁ = 1 + ₁ = 1 - 2 1=1-2/2² - Oy₂ = 1 + Oy₁ = 1- x ² + 3x8 8 3x4 8 11x4 24 3x4 8 19x12 80 19x6 80 + 77x5 240 19x6 80 + 1 +... and y₂ = x + x³ +. and and and and Y₂ = x + - Y₂= = x + Y₂ Y₂ 2x³ 3 = x + 4x5 5 2x5 7x⁹ 15 3 = x + x³ + + + 7x5 15 + + 7x5 15 + + 52x7 105 + 4x13 15 4x7 15 + 4x7 15 4x 52x7 5 105 + + +
Find two power series solutions of the given differential equation about the ordinary point x = 0. y" 5xy' + y = 0 + x² + 11x4 + 77x6 2 24 240 Oy₁ = 1 + ₁ = 1 - 2 1=1-2/2² - Oy₂ = 1 + Oy₁ = 1- x ² + 3x8 8 3x4 8 11x4 24 3x4 8 19x12 80 19x6 80 + 77x5 240 19x6 80 + 1 +... and y₂ = x + x³ +. and and and and Y₂ = x + - Y₂= = x + Y₂ Y₂ 2x³ 3 = x + 4x5 5 2x5 7x⁹ 15 3 = x + x³ + + + 7x5 15 + + 7x5 15 + + 52x7 105 + 4x13 15 4x7 15 + 4x7 15 4x 52x7 5 105 + + +
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" 5xy' + y = 0
+ x² + 11x4 + 77x6
2
24
240
Oy₁ = 1 +
₁ = 1
-
2
1=1-2/2² -
Oy₂ = 1 +
Oy₁ = 1-
x ²
+
3x8
8
3x4
8
11x4
24
3x4
8
19x12
80
19x6
80
+
77x5
240
19x6
80
+
1
+...
and y₂ = x + x³ +.
and
and
and
and
Y₂ = x +
-
Y₂= = x +
Y₂
Y₂
2x³
3
= x +
4x5
5
2x5 7x⁹
15
3
= x + x³ +
+
+
7x5
15
+
+
7x5
15
+
+
52x7
105
+
4x13
15
4x7
15
+
4x7
15
4x 52x7
5
105
+
+
+
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