5.2 Series Solutions Near an Ordin Problems In each of Problems 1 through 6, determine the radius of convergence of the given power series. 15. Let y a,x". 1. (x-3)" n=0 a. Compute y' and y and write out the series, as well as the coefficient of x" in th b. Show that if y = y, then the coef arbitrary, and determine c. Show that an+2= n=0 n 2. 2n n=0 az and an in term (n+2)(n+1) 3. n! In each of Problems 16 and 17, verify the giver n=0 = a,-1(x-1) 4. 2"x" 16. an(x-1)+1 n=0 n=1 n=0 (x- xo)" Σαx +Σ απ =α+ Σ. 17. ak+ 5. k-1 k-0 k 0 n n=1 In each of Problems 18 through 22, rewrite the single power series whose generic term involve 1)"n2(x+ 2)" 6. 31 n=1 E 1)a.r-2 18. n(n ah of Prohlems 7 through 13, determine the Taylor series about ni
5.2 Series Solutions Near an Ordin Problems In each of Problems 1 through 6, determine the radius of convergence of the given power series. 15. Let y a,x". 1. (x-3)" n=0 a. Compute y' and y and write out the series, as well as the coefficient of x" in th b. Show that if y = y, then the coef arbitrary, and determine c. Show that an+2= n=0 n 2. 2n n=0 az and an in term (n+2)(n+1) 3. n! In each of Problems 16 and 17, verify the giver n=0 = a,-1(x-1) 4. 2"x" 16. an(x-1)+1 n=0 n=1 n=0 (x- xo)" Σαx +Σ απ =α+ Σ. 17. ak+ 5. k-1 k-0 k 0 n n=1 In each of Problems 18 through 22, rewrite the single power series whose generic term involve 1)"n2(x+ 2)" 6. 31 n=1 E 1)a.r-2 18. n(n ah of Prohlems 7 through 13, determine the Taylor series about ni
Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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How do I determine the radius of convergence for problem #6? This is from my differential equations textbook, and this section is titled, "Review of Power Series."
Transcribed Image Text:5.2 Series Solutions Near an Ordin
Problems
In each of Problems 1 through 6, determine the radius of convergence
of the given power series.
15. Let y a,x".
1. (x-3)"
n=0
a. Compute y' and y and write out the
series, as well as the coefficient of x" in th
b. Show that if y = y, then the coef
arbitrary, and determine
c. Show that an+2=
n=0
n
2.
2n
n=0
az and
an
in term
(n+2)(n+1)
3.
n!
In each of Problems 16 and 17, verify the giver
n=0
= a,-1(x-1)
4. 2"x"
16.
an(x-1)+1
n=0
n=1
n=0
(x- xo)"
Σαx +Σ απ =α+ Σ.
17.
ak+
5.
k-1
k-0
k 0
n
n=1
In each of Problems 18 through 22, rewrite the
single power series whose generic term involve
1)"n2(x+ 2)"
6.
31
n=1
E
1)a.r-2
18.
n(n
ah of Prohlems 7 through 13, determine the Taylor series about
ni
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