x^2y" + x (1−x)y' − xy = 0. a. Show that X0=0 is a regular singular point. b. Determine the indicial equation, the recurrence relation, and the roots of the indicial equation. c. Find the series
x^2y" + x (1−x)y' − xy = 0. a. Show that X0=0 is a regular singular point. b. Determine the indicial equation, the recurrence relation, and the roots of the indicial equation. c. Find the series
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
x^2y" + x (1−x)y' − xy = 0.
- a. Show that X0=0 is a regular singular point.
- b. Determine the indicial equation, the recurrence relation, and the roots of the indicial equation.
- c. Find the series solution for x>0 corresponding to the larger root.
- d. Find the series solution corresponding to the smaller root by following the procedure outlined in section 5.4 and demonstrated in section 5.7.
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