The critical points of the nonlinear differential equation θ ″ + sin θ = 1 2 are ( π 6 , 0 ) and ( 5 π 6 , 0 ) .

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Answer 1

Question

Chapter 11.3, Problem 39E

(a)

To determine

To show: The critical points of the nonlinear differential equation θ″+sinθ=12 are (π6,0) and (5π6,0).

(b)

To determine

The nature of the critical point (5π6,0) by linearization.

(c)

To determine

The nature of the critical point (π6,0) by phase plane method.

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Answer 2

Question

Chapter 11.3, Problem 39E

(a)

To determine

To show: The critical points of the nonlinear differential equation θ″+sinθ=12 are (π6,0) and (5π6,0).

(b)

To determine

The nature of the critical point (5π6,0) by linearization.

(c)

To determine

The nature of the critical point (π6,0) by phase plane method.

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Answer 3

Question

Chapter 11.3, Problem 39E

(a)

To determine

To show: The critical points of the nonlinear differential equation θ″+sinθ=12 are (π6,0) and (5π6,0).

(b)

To determine

The nature of the critical point (5π6,0) by linearization.

(c)

To determine

The nature of the critical point (π6,0) by phase plane method.

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Answer 4

Question

Chapter 11.3, Problem 39E

(a)

To determine

To show: The critical points of the nonlinear differential equation θ″+sinθ=12 are (π6,0) and (5π6,0).

(b)

To determine

The nature of the critical point (5π6,0) by linearization.

(c)

To determine

The nature of the critical point (π6,0) by phase plane method.

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Answer 5

Chapter 11.3, Problem 39E

(a)

To determine

To show: The critical points of the nonlinear differential equation θ″+sinθ=12 are (π6,0) and (5π6,0).

(b)

To determine

The nature of the critical point (5π6,0) by linearization.

(c)

To determine

The nature of the critical point (π6,0) by phase plane method.

Answer 6

Chapter 11.3, Problem 39E

(a)

To determine

To show: The critical points of the nonlinear differential equation θ″+sinθ=12 are (π6,0) and (5π6,0).

Answer 7

Chapter 11.3, Problem 39E

(a)

To determine

To show: The critical points of the nonlinear differential equation θ″+sinθ=12 are (π6,0) and (5π6,0).

Answer 8

(b)

To determine

The nature of the critical point (5π6,0) by linearization.

Answer 9

(b)

To determine

The nature of the critical point (5π6,0) by linearization.

Answer 10

(c)

To determine

The nature of the critical point (π6,0) by phase plane method.

Answer 11

(c)

To determine

The nature of the critical point (π6,0) by phase plane method.

Answer 12

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Answer 13

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Answer 14

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Answer 15

Ch. 11.1 - Prob. 1E Ch. 11.1 - Prob. 2E Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E Ch. 11.1 - Prob. 7E Ch. 11.1 - Prob. 8E Ch. 11.1 - Prob. 9E Ch. 11.1 - Prob. 10E

The critical points of the nonlinear differential equation θ ″ + sin θ = 1 2 are ( π 6 , 0 ) and ( 5 π 6 , 0 ) .

Solution Summary: The author explains the critical points of the nonlinear differential equation theta =12 and the system of differential formed as follows:

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To show: The critical points of the nonlinear differential equation θ″+sinθ=12 are (π6,0) and (5π6,0).

The nature of the critical point (5π6,0) by linearization.

The nature of the critical point (π6,0) by phase plane method.

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