Let the differential equation y" +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 to = 0. Find the first five terms only. (d) Guess a power series solution to the differential equation ry" +3y = 0 of the form y = 2 an (x – 1)" (the first five terms only). n=0

Let the differential equation y" +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 to = 0. Find the first five terms only. (d) Guess a power series solution to the differential equation ry" +3y = 0 of the form y = 2 an (x – 1)" (the first five terms only). n=0

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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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

Let the differential equation ry" + 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 involvingt and y(t).
(c) Find a power series solution of the differential equation you obtained in part (b) about
to = 0. Find the first five terms only.
(d) Guess a power series solution to the differential equation ry" + 3y = 0 of the form y =
> an(x – 1)" (the first five terms only).
n=0

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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).