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 10.3, 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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Q/By using Hart man theorem study the Stability of the critical points and draw the phase portrait of the system:- X = -4x+2xy - 8 y° = 4y² X2

This means that when the Radius of Convergence of the Power Series is a "finite positive real number" r>0, then every point x of the Power Series on (-r, r) will absolutely converge (x ∈ (-r, r)). Moreover, every point x on the Power Series (-∞, -r)U(r, +∞) will diverge (|x| >r). Please explain it.

Answer 2

Question

Chapter 10.3, 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 10.3, 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 10.3, 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 10.3, 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 10.3, 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 10.3, 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. 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 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.

Solution Summary: The author explains the critical points for the plane autonomous system of equations xprime,y, and describes their nature 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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