Solve for the general solution using the Power Series. The answers were already given, you just have to provide the solutions. TEST YOUR UNDERSTANDING! ANSWER KEY-Find the G.S. about xo = 0 for the following DE's1. (x²+4)y" + 2xy' - 12y = 0805Answer: y = a₁ + a₁x +29₁x²³ +(-1)k (k+1)3aox²k22k (2k-3)(2k-1)k=12. (1+x²)y" + 10xy' + 20y = 0Answer: y = a + a₁x +(−1)k (2k + 1)(2k + 3)(k+1)α₁x²k,3k=13. (x² + 4)y" + xy = x + 21-aoAnswer: y =a₁ + 2Laanx"=244872=0ao + a₁x + = x² +-x3(−1)k(k+ 1)(k+ 2)(2k + 3) a₁x²k+162-ao3202²x5

Since you have asked multiple question. According to our guidelines we will solve the first…

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

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Question

Solve for the general solution using the Power Series. The answers were already given, you just have to provide the solutions.

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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