The Bernoulli differential equation d y d x = − y − x y − 1 is obtained when phase plane method is applied on the differential equation x ″ + ( x ′ ) 2 + x = 0 .

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Answer 1

Question

Chapter 10.3, Problem 34E

(a)

To determine

To show: The Bernoulli differential equation dydx=−y−xy−1 is obtained when phase plane method is applied on the differential equation x″+(x′)2+x=0.

(b)

To determine

To show: The solution of the differential equation x″+(x′)2+x=0 which satisfies the condition x′(0)=0 and x(0)=12 is not periodic.

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Answer 2

Question

Chapter 10.3, Problem 34E

(a)

To determine

To show: The Bernoulli differential equation dydx=−y−xy−1 is obtained when phase plane method is applied on the differential equation x″+(x′)2+x=0.

(b)

To determine

To show: The solution of the differential equation x″+(x′)2+x=0 which satisfies the condition x′(0)=0 and x(0)=12 is not periodic.

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Answer 3

Question

Chapter 10.3, Problem 34E

(a)

To determine

To show: The Bernoulli differential equation dydx=−y−xy−1 is obtained when phase plane method is applied on the differential equation x″+(x′)2+x=0.

(b)

To determine

To show: The solution of the differential equation x″+(x′)2+x=0 which satisfies the condition x′(0)=0 and x(0)=12 is not periodic.

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Answer 4

Question

Chapter 10.3, Problem 34E

(a)

To determine

To show: The Bernoulli differential equation dydx=−y−xy−1 is obtained when phase plane method is applied on the differential equation x″+(x′)2+x=0.

(b)

To determine

To show: The solution of the differential equation x″+(x′)2+x=0 which satisfies the condition x′(0)=0 and x(0)=12 is not periodic.

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Answer 5

Chapter 10.3, Problem 34E

(a)

To determine

To show: The Bernoulli differential equation dydx=−y−xy−1 is obtained when phase plane method is applied on the differential equation x″+(x′)2+x=0.

(b)

To determine

To show: The solution of the differential equation x″+(x′)2+x=0 which satisfies the condition x′(0)=0 and x(0)=12 is not periodic.

Answer 6

Chapter 10.3, Problem 34E

(a)

To determine

To show: The Bernoulli differential equation dydx=−y−xy−1 is obtained when phase plane method is applied on the differential equation x″+(x′)2+x=0.

Answer 7

Chapter 10.3, Problem 34E

(a)

To determine

To show: The Bernoulli differential equation dydx=−y−xy−1 is obtained when phase plane method is applied on the differential equation x″+(x′)2+x=0.

Answer 8

(b)

To determine

To show: The solution of the differential equation x″+(x′)2+x=0 which satisfies the condition x′(0)=0 and x(0)=12 is not periodic.

Answer 9

(b)

To determine

To show: The solution of the differential equation x″+(x′)2+x=0 which satisfies the condition x′(0)=0 and x(0)=12 is not periodic.

Answer 10

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Answer 11

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Answer 12

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Answer 13

Ch. 10.1 - In Problems 16 write the given nonlinear...Ch. 10.1 - Prob. 2E Ch. 10.1 - In Problems 16 write the given nonlinear...Ch. 10.1 - Prob. 4E Ch. 10.1 - In Problems 16 write the given nonlinear...Ch. 10.1 - In Problems 16 write the given nonlinear...Ch. 10.1 - Prob. 7E Ch. 10.1 - Prob. 8E Ch. 10.1 - Prob. 9E Ch. 10.1 - Prob. 10E

The Bernoulli differential equation d y d x = − y − x y − 1 is obtained when phase plane method is applied on the differential equation x ″ + ( x ′ ) 2 + x = 0 .

Solution Summary: The author explains that the Bernoulli differential equation is obtained when phase plane method is applied.

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To show: The Bernoulli differential equation dydx=−y−xy−1 is obtained when phase plane method is applied on the differential equation x″+(x′)2+x=0.

To show: The solution of the differential equation x″+(x′)2+x=0 which satisfies the condition x′(0)=0 and x(0)=12 is not periodic.

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