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Legendre's DE is (1-x²) y" – 2x y' + ày = 0. (a) Show that x = 0 is an ordinary point of this DE. (b) For solutions, y = >, a, x", the recurrence relation п (п+1)—2 (n+2)(n+1) Find the first 4 values of 1 such that the series n=0 connecting the coefficients is a,+2 terminates and yields a polynomial solution. (c ) Taking ao 1 and = 1 find the first 4 polynomial solutions.

Legendre's DE is (1-x²) y" – 2x y' + ày = 0. (a) Show that x = 0 is an ordinary point of this DE. (b) For solutions, y = >, a, x", the recurrence relation п (п+1)—2 (n+2)(n+1) Find the first 4 values of 1 such that the series n=0 connecting the coefficients is a,+2 terminates and yields a polynomial solution. (c ) Taking ao 1 and = 1 find the first 4 polynomial solutions.

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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Legendre's DE is (1-x²) y" – 2x y' + ày = 0. (a) Show that x = 0 is an ordinary point of this DE. (b) For solutions, y = >, a, x", the recurrence relation п (п+1)—2 (n+2)(n+1) Find the first 4 values of 1 such that the series n=0 connecting the coefficients is a,+2 terminates and yields a polynomial solution. (c ) Taking ao 1 and = 1 find the first 4 polynomial solutions.
Transcribed Image Text:Legendre's DE is (1-x²) y" – 2x y' + ày = 0. (a) Show that x = 0 is an ordinary point of this DE. (b) For solutions, y = >, a, x", the recurrence relation п (п+1)—2 (n+2)(n+1) Find the first 4 values of 1 such that the series n=0 connecting the coefficients is a,+2 terminates and yields a polynomial solution. (c ) Taking ao 1 and = 1 find the first 4 polynomial solutions.
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