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Problem 2 a) The fundamental solutions to the Legendre equation are: Y₁(x) = 1 - y₂(x) = x (n-1)(n + 2) 3! Show that when n = 0 Y₁(x) = 1 1- n(n+1) 2! y2(x) = x + 1 3 +. 5 2 x² + + (n − 2)n(n + 1)(n + 3) 4! + (n-3)(n T X 4 - +... 1)(n + 2)(n + 4) 5! x5 3 b) Solve the Legendre equation using separation of variables for n=0. Legendre equation: (1-x²)y" - 2xy' + n(n + 1)y = 0 +.. (n constant)

Problem 2 a) The fundamental solutions to the Legendre equation are: Y₁(x) = 1 - y₂(x) = x (n-1)(n + 2) 3! Show that when n = 0 Y₁(x) = 1 1- n(n+1) 2! y2(x) = x + 1 3 +. 5 2 x² + + (n − 2)n(n + 1)(n + 3) 4! + (n-3)(n T X 4 - +... 1)(n + 2)(n + 4) 5! x5 3 b) Solve the Legendre equation using separation of variables for n=0. Legendre equation: (1-x²)y" - 2xy' + n(n + 1)y = 0 +.. (n constant)

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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Problem 2 a) The fundamental solutions to the Legendre equation are: Y₁(x) = 1 - 1 n(n+1) 2! y2(x) = x + (n-1)(n+ 2) y₂(x) = x 3! Show that when n = 0 Y₁(x) = 1 1 3 +. 5 x² + 2 + (n − 2)n(n + 1)(n + 3) 4! + (n − 3)(n T X 4 - +... 1)(n + 2)(n + 4) 5! x5 3 b) Solve the Legendre equation using separation of variables for n=0. Legendre equation: (1-x²)y" - 2xy' + n(n + 1)y = 0 +. (n constant)
Transcribed Image Text:Problem 2 a) The fundamental solutions to the Legendre equation are: Y₁(x) = 1 - 1 n(n+1) 2! y2(x) = x + (n-1)(n+ 2) y₂(x) = x 3! Show that when n = 0 Y₁(x) = 1 1 3 +. 5 x² + 2 + (n − 2)n(n + 1)(n + 3) 4! + (n − 3)(n T X 4 - +... 1)(n + 2)(n + 4) 5! x5 3 b) Solve the Legendre equation using separation of variables for n=0. Legendre equation: (1-x²)y" - 2xy' + n(n + 1)y = 0 +. (n constant)
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