Consider the following differential equation: x?(1 – 2x)y" + 3xy' + (1 + 4x)y = 0 (2) (a) Find the singular and ordinary points of Equation (2). Next, show that xo = 0 is a regular singular point of Equation (2).

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.1: Solutions Of Elementary And Separable Differential Equations
Problem 15E: Find the general solution for each differential equation. Verify that each solution satisfies the...
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Determine the series solutions of Equation (2) at the regular singular
point x, = 0 using suitable method. Show details of your work indicating
(b)
the indicial equation, roots of indicial equation, and the recurrence
relation, where relevant.
Transcribed Image Text:Determine the series solutions of Equation (2) at the regular singular point x, = 0 using suitable method. Show details of your work indicating (b) the indicial equation, roots of indicial equation, and the recurrence relation, where relevant.
Consider the following differential equation:
х? (1 — 2х)у" + 3хy' + (1 + 4x)у — 0
(2)
(a)
Find the singular and ordinary points of Equation (2). Next, show that
xo = 0 is a regular singular point of Equation (2).
2.
Transcribed Image Text:Consider the following differential equation: х? (1 — 2х)у" + 3хy' + (1 + 4x)у — 0 (2) (a) Find the singular and ordinary points of Equation (2). Next, show that xo = 0 is a regular singular point of Equation (2). 2.
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