Let the differential equation xy'' + 3y = 0. (a) What are the ordinary points of the differential equation? (b) Use the change of variable t = x − 1 to rewrite the differential equation as a second-order differential equation involving t and y(t). (c) Find a power series solution of the differential equation you obtained in part (b) about t0 = 0. Find the first five terms only. (d) Guess a power series solution to the differential equation xy''+ 3y = 0 of the form y = X∞ n=0 an(x − 1)n (the first five terms only).
Let the differential equation xy'' + 3y = 0. (a) What are the ordinary points of the differential equation? (b) Use the change of variable t = x − 1 to rewrite the differential equation as a second-order differential equation involving t and y(t). (c) Find a power series solution of the differential equation you obtained in part (b) about t0 = 0. Find the first five terms only. (d) Guess a power series solution to the differential equation xy''+ 3y = 0 of the form y = X∞ n=0 an(x − 1)n (the first five terms only).
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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Let the differential equation xy'' + 3y = 0.
(a) What are the ordinary points of the differential equation?
(b) Use the change of variable t = x − 1 to rewrite the differential equation as a second-order
differential equation involving t and y(t).
(c) Find a power series solution of the differential equation you obtained in part (b) about
t0 = 0. Find the first five terms only.
(d) Guess a power series solution to the differential equation xy''+ 3y = 0 of the form y = X∞
n=0
an(x − 1)n
(the first five terms only).
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