Answered: x^2y" + x (1−x)y' − xy = 0. a. Show…

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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Question

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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