TEST YOUR UNDERSTANDING! ANSWER KEY- Find the G.S. about xo = 0 for the following DE's 1. (x²+4)y" + 2xy' - 12y = 0 5 Answer: y = a₁ + a₁x + 129₁x² + 2x2(x+1)34x2k (2k-3)(2k-1) k=1 2. (1+x²)y" + 10xy' + 20y = 0 (-1) (2k + 1)(2k + 3)(k+1) aox2k. (−1)k(k+ 1)(k+ 2)(2k + 3)a₂x²k+1 Answer: y = a + a₁x + 3 6 k=1 3. (x²+4)y" + xy = x+2 a₁ + Answer: y = -Σanx ao + a₁x 1-ao. 24 48 712=0 1 - 2-a 320 ²x² +. ***
TEST YOUR UNDERSTANDING! ANSWER KEY- Find the G.S. about xo = 0 for the following DE's 1. (x²+4)y" + 2xy' - 12y = 0 5 Answer: y = a₁ + a₁x + 129₁x² + 2x2(x+1)34x2k (2k-3)(2k-1) k=1 2. (1+x²)y" + 10xy' + 20y = 0 (-1) (2k + 1)(2k + 3)(k+1) aox2k. (−1)k(k+ 1)(k+ 2)(2k + 3)a₂x²k+1 Answer: y = a + a₁x + 3 6 k=1 3. (x²+4)y" + xy = x+2 a₁ + Answer: y = -Σanx ao + a₁x 1-ao. 24 48 712=0 1 - 2-a 320 ²x² +. ***
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
Solve for the general solution using the Power Series. The answers were already given, you just have to provide the solutions.
Transcribed Image Text:TEST YOUR UNDERSTANDING! ANSWER KEY-
Find the G.S. about xo = 0 for the following DE's
1. (x²+4)y" + 2xy' - 12y = 0
80
5
Answer: y = a₁ + a₁x +29₁x²³ +
(-1)k (k+1)3aox²k
22k (2k-3)(2k-1)
k=1
2. (1+x²)y" + 10xy' + 20y = 0
Answer: y = a + a₁x +
(−1)k (2k + 1)(2k + 3)(k+1)α₁x²k,
3
k=1
3. (x² + 4)y" + xy = x + 2
1-ao
Answer: y =
a₁ + 2
La
anx"=
24
48
72=0
ao + a₁x + = x² +
-x3
(−1)k(k+ 1)(k+ 2)(2k + 3) a₁x²k+1
6
2-ao
320
2²x5
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