Solve the following ordinary differential equations using the power series method: y"-9y=0 Example solutions is in the picture.

Calculus: Early Transcendentals
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Author:James Stewart
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Chapter1: Functions And Models
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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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Solve the following ordinary differential equations using the power series method: y"-9y=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
Transcribed Image Text: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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