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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
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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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
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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