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Consider the following differential equation: r*(1– 2x)y" + 3xy' +(1+4x)y = 0 (2) a) Find the singular and ordinary points of Equation (2). Next, show that x, = 0 is a regular singular point of Equation (2). (b) Determine the series solutions of Equation (2) at the regular singular point x, = 0 using suitable method. Show details of your work indicating the indicial equation, roots of indicial equation, and the recurrence relation, where relevant.

Consider the following differential equation: r*(1– 2x)y" + 3xy' +(1+4x)y = 0 (2) a) Find the singular and ordinary points of Equation (2). Next, show that x, = 0 is a regular singular point of Equation (2). (b) Determine the series solutions of Equation (2) at the regular singular point x, = 0 using suitable method. Show details of your work indicating the indicial equation, roots of indicial equation, and the recurrence relation, where relevant.

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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2. Consider the following differential equation: x²(1 – 2x)y" + 3xy' + (1+ 4x)y = 0 (2) Find the singular and ordinary points of Equation (2). Next, show that x, = 0 is a regular singular point of Equation (2). (a) (b) Determine the series solutions of Equation (2) at the regular singular point x, = 0 using suitable method. Show details of your work indicating the indicial equation, roots of indicial equation, and the recurrence relation, where relevant.
Transcribed Image Text:2. Consider the following differential equation: x²(1 – 2x)y" + 3xy' + (1+ 4x)y = 0 (2) Find the singular and ordinary points of Equation (2). Next, show that x, = 0 is a regular singular point of Equation (2). (a) (b) Determine the series solutions of Equation (2) at the regular singular point x, = 0 using suitable method. Show details of your work indicating the indicial equation, roots of indicial equation, and the recurrence relation, where relevant.
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