siven the power series expression E A_ x(m + 1) A x" n = 1 = 3 1. Force the first power series to have a simple exponent. 2. Make sure that the power series start at the same value for n. 3. Combine the two power series together into a single power series. ® A, x! + E [A« - ) + A ]: R = 2 ® 4,x' + A,x² + £ [24, ] ** R = 3 + A,]* R R = 1 © (4, + A,) =' + Ž [^«•, + A,]«* (4, + A,) x! (R + R= 2
siven the power series expression E A_ x(m + 1) A x" n = 1 = 3 1. Force the first power series to have a simple exponent. 2. Make sure that the power series start at the same value for n. 3. Combine the two power series together into a single power series. ® A, x! + E [A« - ) + A ]: R = 2 ® 4,x' + A,x² + £ [24, ] ** R = 3 + A,]* R R = 1 © (4, + A,) =' + Ž [^«•, + A,]«* (4, + A,) x! (R + R= 2
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
q1
![Given the power series expression
00
E 4, xln + 1)
> A x"
n = 3
n = 1
1. Force the first power series to have a simple exponent.
2. Make sure that the power series start at the same value for n.
3. Combine the two power series together into a single power series.
00
A A, x' +
(R – 1) + AR x*
R = 2
+ A,x? + E [24, ] *
R = 3
00
Σ
+ A
R
(R+ 1)
R = 1
O (4, + A,) + £ [^.*^]"
R = 2
ΘΣ
E [24, ] **
R
R = 1
F
(R - 1) + AR *
R = 0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F25002bdf-f87e-4b90-9220-df81045dfb4e%2Fdc4a665a-d161-41d3-b6d0-7be6e666d214%2Frisi1mo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Given the power series expression
00
E 4, xln + 1)
> A x"
n = 3
n = 1
1. Force the first power series to have a simple exponent.
2. Make sure that the power series start at the same value for n.
3. Combine the two power series together into a single power series.
00
A A, x' +
(R – 1) + AR x*
R = 2
+ A,x? + E [24, ] *
R = 3
00
Σ
+ A
R
(R+ 1)
R = 1
O (4, + A,) + £ [^.*^]"
R = 2
ΘΣ
E [24, ] **
R
R = 1
F
(R - 1) + AR *
R = 0
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