Consider the following differential equation, 5xy" + (1+x) y' + 2y: = 0. Note that xo = 0 is a regular singular point. Suppose that we look for a series solution of the form y = Σcnxn+r. n=0 (a) Find the two roots of the indicial equation. (b) The recurrence formula for the coefficients of the solution with the larger root is given by Ck+1 = g(k) ck, k ≥ 0. Enter the function g(k) into the answer box below. (c) Taking co = 1, find the first 3 terms of the solution corresponding to the largest root.
Consider the following differential equation, 5xy" + (1+x) y' + 2y: = 0. Note that xo = 0 is a regular singular point. Suppose that we look for a series solution of the form y = Σcnxn+r. n=0 (a) Find the two roots of the indicial equation. (b) The recurrence formula for the coefficients of the solution with the larger root is given by Ck+1 = g(k) ck, k ≥ 0. Enter the function g(k) into the answer box below. (c) Taking co = 1, find the first 3 terms of the solution corresponding to the largest root.
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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Transcribed Image Text:Consider the following differential equation,
5xy" + (1 + x) y' + 2y 0.
Note that xo
=
0 is a regular singular point. Suppose that we look for a series solution of the form
y = 2 cxtr.
n=0
(a) Find the two roots of the indicial equation.
(b) The recurrence formula for the coefficients of the solution with the larger root is given by
g(k) ck, k ≥ 0. Enter the function g(k) into the answer box below.
Ck+1
(c) Taking co
=
1, find the first 3 terms of the solution corresponding to the largest root.
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