Show the solutions. Find the G.S. about x, = 0 for the following DE's1.(x² + 4)y" + 2xy' – 12y = 0(-1)*(k + 1)3a,x 2k2k (2k – 3)(2k – 1)5Answer: y = a, + a,x +za;x³ +k=12.(1 + x²)y" + 10xy' + 20y = 0(-1)*(2k + 1)(2k + 3)(k + 1)a,x²k -3(-1)*(k + 1)(k + 2)(2k + 3)a,x2k+1Answer: y = a, + a,x +k=1k=13.(x² + 4)y" + xy = x + 211- aoAnswer: y = > anx" = a, + a,x +7x² +2 - aox5 + ·320...2448n=0

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Find the G.S. about x, = 0 for the following DE's 1. (x² + 4)y" + 2xy' – 12y = 0

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter5: Polynomial And Rational Functions

Section: Chapter Questions

Problem 27PT: Find the unknown value. 27. y varies jointly with x and the cube root of 2. If when x=2 and...

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Question

Show the solutions.

Find the G.S. about x, = 0 for the following DE's
1.
(x² + 4)y" + 2xy' – 12y = 0
(-1)*(k + 1)3a,x 2k
2k (2k – 3)(2k – 1)
5
Answer: y = a, + a,x +za;x³ +
k=1
2.
(1 + x²)y" + 10xy' + 20y = 0
(-1)*(2k + 1)(2k + 3)(k + 1)a,x²k -
3
(-1)*(k + 1)(k + 2)(2k + 3)a,x2k+1
Answer: y = a, + a,x +
k=1
k=1
3.
(x² + 4)y" + xy = x + 2
1
1- ao
Answer: y = > anx" = a, + a,x +7x² +
2 - ao
x5 + ·
320
...
24
48
n=0

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