6. (6.2) Find two power series solutions of the differential equation y" - xy' +2y = o about the ordinary point x = 0. 1 1 Y1 = 1-r? and 92 = r- 6 120
6. (6.2) Find two power series solutions of the differential equation y" - xy' +2y = o about the ordinary point x = 0. 1 1 Y1 = 1-r? and 92 = r- 6 120
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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Question 6 has been answered. The answer is correct. Please explain how to get said answer. The power series table has been provided in case you need it.
Transcribed Image Text:6. (6.2) Find two power series solutions of the differential equation
y" - xy' +2y = o about the ordinary point x = 0.
1.
1
Y1 = 1– r²
and
42 = r -r*
120
![Interval
Maclaurin Series
of Convergence
e* = 1 +
1!
Σ
(-00, 00)
2!
3!
-o n!
x2
cos x = 1
(-1)"
(-0, 0)
....
2!
4!
6!
N=0 (2n)!
(-1)"
Σ
(2n + 1)!
sin x = x -
3!
(-0, 00)
5!
7!
0
x x7
(-1)"
tan x = x -
[-1, 1]
(2)
2n + 1
0
= 1 +
2!
(-0, 0)
cosh x
+
6!
, (2n)!
4!
x7
1
Σ
(2n + 1)!
sinh x = x +
+
5!
3!
(-0, 0)
+... =
7!
=0
x?
In(1 + x) = x -
(-1)"+1
(-1, 1]
3
4
1+ x+ x?
(-1, 1)
....
n=0
+
+
+](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F07b0abd5-8e11-4199-867f-91e48391320a%2F0ea8a79d-6d99-4d14-8db3-ca8297d72a92%2Fs91sbr4_processed.png&w=3840&q=75)
Transcribed Image Text:Interval
Maclaurin Series
of Convergence
e* = 1 +
1!
Σ
(-00, 00)
2!
3!
-o n!
x2
cos x = 1
(-1)"
(-0, 0)
....
2!
4!
6!
N=0 (2n)!
(-1)"
Σ
(2n + 1)!
sin x = x -
3!
(-0, 00)
5!
7!
0
x x7
(-1)"
tan x = x -
[-1, 1]
(2)
2n + 1
0
= 1 +
2!
(-0, 0)
cosh x
+
6!
, (2n)!
4!
x7
1
Σ
(2n + 1)!
sinh x = x +
+
5!
3!
(-0, 0)
+... =
7!
=0
x?
In(1 + x) = x -
(-1)"+1
(-1, 1]
3
4
1+ x+ x?
(-1, 1)
....
n=0
+
+
+
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