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1: Consider the following differential equation, 5xy"' + (2 + x) y + y = 0. Note that xo = 0 is a regular singular point. Suppose that we look for a series solution of the form y = [ n=0 Cnx+r (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.

1: Consider the following differential equation, 5xy"' + (2 + x) y + y = 0. Note that xo = 0 is a regular singular point. Suppose that we look for a series solution of the form y = [ n=0 Cnx+r (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.

Calculus For The Life Sciences
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.CR: Chapter 11 Review
Problem 15CR
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#11: Consider the following differential equation, 5xy' +(2+x) y + y = 0. Note that x = 0 is a regular singular point. Suppose that we look for a series solution of the form y = Σ n=0 Cnxn+r (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.
Transcribed Image Text:#11: Consider the following differential equation, 5xy' +(2+x) y + y = 0. Note that x = 0 is a regular singular point. Suppose that we look for a series solution of the form y = Σ n=0 Cnxn+r (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.
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