The critical points for the plane autonomous system of equations x ′ = 2 x y , y ′ = 1 − x 2 + y 2 and describe the nature of critical points by linearization.

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Answer 1

Question

Chapter 11.3, Problem 33E

(a)

To determine

The critical points for the plane autonomous system of equations x′=2xy, y′=1−x2+y2 and describe the nature of critical points by linearization.

(b)

To determine

The verification of critical points of plane autonomous system of equations x′=2xy, y′=1−x2+y2 are both centers of the solution curves.

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Answer 2

Question

Chapter 11.3, Problem 33E

(a)

To determine

The critical points for the plane autonomous system of equations x′=2xy, y′=1−x2+y2 and describe the nature of critical points by linearization.

(b)

To determine

The verification of critical points of plane autonomous system of equations x′=2xy, y′=1−x2+y2 are both centers of the solution curves.

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Answer 3

Question

Chapter 11.3, Problem 33E

(a)

To determine

The critical points for the plane autonomous system of equations x′=2xy, y′=1−x2+y2 and describe the nature of critical points by linearization.

(b)

To determine

The verification of critical points of plane autonomous system of equations x′=2xy, y′=1−x2+y2 are both centers of the solution curves.

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Answer 4

Question

Chapter 11.3, Problem 33E

(a)

To determine

The critical points for the plane autonomous system of equations x′=2xy, y′=1−x2+y2 and describe the nature of critical points by linearization.

(b)

To determine

The verification of critical points of plane autonomous system of equations x′=2xy, y′=1−x2+y2 are both centers of the solution curves.

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Answer 5

Chapter 11.3, Problem 33E

(a)

To determine

The critical points for the plane autonomous system of equations x′=2xy, y′=1−x2+y2 and describe the nature of critical points by linearization.

(b)

To determine

The verification of critical points of plane autonomous system of equations x′=2xy, y′=1−x2+y2 are both centers of the solution curves.

Answer 6

Chapter 11.3, Problem 33E

(a)

To determine

The critical points for the plane autonomous system of equations x′=2xy, y′=1−x2+y2 and describe the nature of critical points by linearization.

Answer 7

Chapter 11.3, Problem 33E

(a)

To determine

The critical points for the plane autonomous system of equations x′=2xy, y′=1−x2+y2 and describe the nature of critical points by linearization.

Answer 8

(b)

To determine

The verification of critical points of plane autonomous system of equations x′=2xy, y′=1−x2+y2 are both centers of the solution curves.

Answer 9

(b)

To determine

The verification of critical points of plane autonomous system of equations x′=2xy, y′=1−x2+y2 are both centers of the solution curves.

Answer 10

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Answer 11

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Answer 12

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Answer 13

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 for the plane autonomous system of equations x ′ = 2 x y , y ′ = 1 − x 2 + y 2 and describe the nature of critical points by linearization.

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The critical points for the plane autonomous system of equations x′=2xy, y′=1−x2+y2 and describe the nature of critical points by linearization.

The verification of critical points of plane autonomous system of equations x′=2xy, y′=1−x2+y2 are both centers of the solution curves.

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