Solve the following ordinary differential equations using the power series method:(x+1) y' - (x+2)=0Example solutions is in the picture. Encc,53y'-y = 0(C, + 2Cx + 3C,x + ..)- (C, + C,x + Cx? + ...) = 0Collecting like powers of x:(C)- Co) + (2C, - C,)x + (3C, - C)x? + ... = 0Then,C, - C, 0C, = Co: 20- C, = 0%3D3C,- C, 0C, =32.C, =3.C; =Therefore,y = C, + C, + C,x? + C,x' + ..y = C, + Cyx + C,x? + C+x2y = Co(l + x +2!+ ...)3!y = CoePROBLEM: ISolve the differential equation y" + y = 0 using the power seriesmethod.Tolu

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Answered: Solve the following ordinary…

Solve the following ordinary differential equations using the power series method: (x+1) y' - (x+2)=0 Example solutions is in the picture.

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

Solve the following ordinary differential equations using the power series method: (x+1) y' - (x+2)=0 Example solutions is in the picture.

Encc,
53
y'-y = 0
(C, + 2Cx + 3C,x + ..)- (C, + C,x + Cx? + ...) = 0
Collecting like powers of x:
(C)
- Co) + (2C, - C,)x + (3C, - C)x? + ... = 0
Then,
C, - C, 0
C, = Co
: 20- C, = 0
%3D
3C,- C, 0
C, =
3
2.
C, =
3.
C; =
Therefore,
y = C, + C, + C,x? + C,x' + ..
y = C, + Cyx + C,x? + C+
x2
y = Co(l + x +
2!
+ ...)
3!
y = Coe
PROBLEM: I
Solve the differential equation y" + y = 0 using the power series
method.
Tolu

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