4. Which of the following is a Legendre's equation? a. (1-x²)y" - 2xy' + 3y = 0 b. (1-x²)y" + 2xy' - 6y = 0 c. (1+x²)y" - 2xy' + 3y = 0 d. (1-x²)y" - 2xy' +6y=0
4. Which of the following is a Legendre's equation? a. (1-x²)y" - 2xy' + 3y = 0 b. (1-x²)y" + 2xy' - 6y = 0 c. (1+x²)y" - 2xy' + 3y = 0 d. (1-x²)y" - 2xy' +6y=0
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
Please pick the correct letter/answer and show the solution if needed.
![4. Which of the following is a Legendre's equation?
a. (1-x²)y" - 2xy' + 3y = 0
b. (1-x²)y" + 2xy' - 6y = 0
c. (1+x²)y" - 2xy' + 3y = 0
d. (1-x²)y" - 2xy' +6y=0
5. Find the solution y₁ (x) of the Legendre equation (1-x²)y" - 2xy' + 2y = 0 using power series method.
x4
x6
a. y₁(x) = 1 - x²
x6
3
5
C. Y₁(x) = 1 + x² − ²₁ +
x4
5
b. y₁(x) = 1- x² +
+ ...
d. y₁(x) = 1- x²-3x4 - 5x6 - ...
3
x6
5](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F31dd9cdb-01c9-42ba-af37-5bb6917fd052%2F9cdbd42e-7197-4034-a6f5-76c2938dc8c7%2Fj1dpfja_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4. Which of the following is a Legendre's equation?
a. (1-x²)y" - 2xy' + 3y = 0
b. (1-x²)y" + 2xy' - 6y = 0
c. (1+x²)y" - 2xy' + 3y = 0
d. (1-x²)y" - 2xy' +6y=0
5. Find the solution y₁ (x) of the Legendre equation (1-x²)y" - 2xy' + 2y = 0 using power series method.
x4
x6
a. y₁(x) = 1 - x²
x6
3
5
C. Y₁(x) = 1 + x² − ²₁ +
x4
5
b. y₁(x) = 1- x² +
+ ...
d. y₁(x) = 1- x²-3x4 - 5x6 - ...
3
x6
5
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