༡ 6. Solve the differential equation by means of a power series about the given ordinary point .xo. Find the recurrence relation for the coefficients of the power series, and also write out the first four terms in each of the two fundamental solutions yı (t) and y2(t). (a) y" +2y=0, x0 = 0 (b) y" + xy+2y= 0, x0 = 0 (c) xy"+y+xy = 0, x0 = 1

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section: Chapter Questions
Problem 18T
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6. Solve the differential equation by means of a power series about the given ordinary point .xo. Find
the recurrence relation for the coefficients of the power series, and also write out the first four terms
in each of the two fundamental solutions yı (t) and y2(t).
(a) y" +2y=0, x0 = 0
(b) y" + xy+2y= 0,
x0 = 0
(c) xy"+y+xy = 0,
x0 = 1
Transcribed Image Text:༡ 6. Solve the differential equation by means of a power series about the given ordinary point .xo. Find the recurrence relation for the coefficients of the power series, and also write out the first four terms in each of the two fundamental solutions yı (t) and y2(t). (a) y" +2y=0, x0 = 0 (b) y" + xy+2y= 0, x0 = 0 (c) xy"+y+xy = 0, x0 = 1
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