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Consider the differential equation - 2x(x − 1)y" + 3(x - 1)y - y = 0 which has a regular singular point at x = 0. The indicial equation for x = 0 is 2+1/2 with roots (in increasing order) r₁ = -1/2 and r2=0 r+ 0 = 0 Find the indicated terms of the following series solutions of the differential equation: (a) y=x(6+-6 x+0 x²+0 30 x4 + ...) (b) y=x(7+-7/3 x+-7/15 x²+-7/35 3+-7/63 x+...) The closed form of solution (a) is y = (6(1-x))/(x^(1/2))

Consider the differential equation - 2x(x − 1)y" + 3(x - 1)y - y = 0 which has a regular singular point at x = 0. The indicial equation for x = 0 is 2+1/2 with roots (in increasing order) r₁ = -1/2 and r2=0 r+ 0 = 0 Find the indicated terms of the following series solutions of the differential equation: (a) y=x(6+-6 x+0 x²+0 30 x4 + ...) (b) y=x(7+-7/3 x+-7/15 x²+-7/35 3+-7/63 x+...) The closed form of solution (a) is y = (6(1-x))/(x^(1/2))

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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Consider the differential equation - 2x(x − 1)y" + 3(x - 1)y - y = 0 which has a regular singular point at x = 0. The indicial equation for x = 0 is 2+1/2 with roots (in increasing order) r₁ = -1/2 and r2=0 r+ 0 = 0 Find the indicated terms of the following series solutions of the differential equation: (a) y=x(6+-6 x+0 x²+0 30 x4 + ...) (b) y=x(7+-7/3 x+-7/15 x²+-7/35 3+-7/63 x+...) The closed form of solution (a) is y = (6(1-x))/(x^(1/2))
Transcribed Image Text:Consider the differential equation - 2x(x − 1)y" + 3(x - 1)y - y = 0 which has a regular singular point at x = 0. The indicial equation for x = 0 is 2+1/2 with roots (in increasing order) r₁ = -1/2 and r2=0 r+ 0 = 0 Find the indicated terms of the following series solutions of the differential equation: (a) y=x(6+-6 x+0 x²+0 30 x4 + ...) (b) y=x(7+-7/3 x+-7/15 x²+-7/35 3+-7/63 x+...) The closed form of solution (a) is y = (6(1-x))/(x^(1/2))
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