1. Given the following differential equation y" – xy = 0. (a) Show that the general solution of the differential equation above about r = 0 is 72n+1 y = ao + a1 Σ. 2" (2n + 1)n!" n=0 [Hint: 2 x 4 x ...x 2n = 2"n!] (b) Find the specific solution if y(0) = 1 and y/(0) = 2.
1. Given the following differential equation y" – xy = 0. (a) Show that the general solution of the differential equation above about r = 0 is 72n+1 y = ao + a1 Σ. 2" (2n + 1)n!" n=0 [Hint: 2 x 4 x ...x 2n = 2"n!] (b) Find the specific solution if y(0) = 1 and y/(0) = 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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Please refer to the image below, solve by using power series method
![1. Given the following differential equation
y" – xy' = 0.
(a) Show that the general solution of the differential equation above about r = 0 is
22n+1
y = ao + a1 >
2" (2n + 1)n!"
n=0
[Hint: 2 x 4 x ·.x 2n = 2"n!]
(b) Find the specific solution if y(0) = 1 and y' (0) = 2.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F64bb96bb-3ca4-4d79-84a2-e431200ed881%2F1cbb8422-00ea-4dbf-baa4-c378a2c21e1d%2Fra2ugmu_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Given the following differential equation
y" – xy' = 0.
(a) Show that the general solution of the differential equation above about r = 0 is
22n+1
y = ao + a1 >
2" (2n + 1)n!"
n=0
[Hint: 2 x 4 x ·.x 2n = 2"n!]
(b) Find the specific solution if y(0) = 1 and y' (0) = 2.
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