Hi, I am looking for some help in understanding a differential equations problem to be solved by series methods. y"-3xy'+y=0, y(0)=3, y'(0)=1 My work is attached, but it looks like a2 and a4 are not correct, but not sure why. If you could clearly explain, that would be helpful. Thank you!
Hi, I am looking for some help in understanding a differential equations problem to be solved by series methods. y"-3xy'+y=0, y(0)=3, y'(0)=1 My work is attached, but it looks like a2 and a4 are not correct, but not sure why. If you could clearly explain, that would be helpful. Thank you!
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
100%
Hi, I am looking for some help in understanding a differential equations problem to be solved by series methods.
y"-3xy'+y=0, y(0)=3, y'(0)=1
My work is attached, but it looks like a2 and a4 are not correct, but not sure why. If you could clearly explain, that would be helpful.
Thank you!
![Assumed form!
29₂-190
+
y
=
y' =
ak+z = 3k-1
n=o
0
Ź ann (n-t) xh-z -3x & an nxnt
1=2
n=1
A3 → K=1=
Ź ann (n-1) xn-2 -3% annxn-
n = 2
n=1
94 > K= 2 =
g
y² =
ук
(k+z) (k+1)
an xn
n=1
00
Σ an n(n-1) x-n-2
1=2
an xny
∞Ő
∞
292 + ¾ ann (n-1) xh-x -3% an nxn -190 -121 an xm-0
n=3
M=1
ทะ
k= 1-2
x=n
k=N
Σ
K=1
2az -190=0
2az = 190
9₂ = 1.90² = 1 + 3 = 2/1/20
2
ак
202 - do + 3 [Q₂ (k+z)(k+1) = (3 k-1) ac] x ² = 0
ас
k=
+1.Z anx' =0
n
3 (1)-1
(1+2)(1+1)
os
акт (к+2) (кн) хк -33 ак кх4 +вawk
K=1
Kay
(1)
130
3 (2) - (2/2)
(2+2)(2+1)
+
& ant" =0
n=0
11
2
= 2 = 1
(3)(2) 6 3
5 (2)
(4)(3)
15=5
24
8](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9d5b5049-d8dd-402a-aa3b-0cfd97dc82be%2Fdd1380ef-3ddd-4e35-8ea7-97e988117361%2Fona62t7_processed.png&w=3840&q=75)
Transcribed Image Text:Assumed form!
29₂-190
+
y
=
y' =
ak+z = 3k-1
n=o
0
Ź ann (n-t) xh-z -3x & an nxnt
1=2
n=1
A3 → K=1=
Ź ann (n-1) xn-2 -3% annxn-
n = 2
n=1
94 > K= 2 =
g
y² =
ук
(k+z) (k+1)
an xn
n=1
00
Σ an n(n-1) x-n-2
1=2
an xny
∞Ő
∞
292 + ¾ ann (n-1) xh-x -3% an nxn -190 -121 an xm-0
n=3
M=1
ทะ
k= 1-2
x=n
k=N
Σ
K=1
2az -190=0
2az = 190
9₂ = 1.90² = 1 + 3 = 2/1/20
2
ак
202 - do + 3 [Q₂ (k+z)(k+1) = (3 k-1) ac] x ² = 0
ас
k=
+1.Z anx' =0
n
3 (1)-1
(1+2)(1+1)
os
акт (к+2) (кн) хк -33 ак кх4 +вawk
K=1
Kay
(1)
130
3 (2) - (2/2)
(2+2)(2+1)
+
& ant" =0
n=0
11
2
= 2 = 1
(3)(2) 6 3
5 (2)
(4)(3)
15=5
24
8
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 3 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
