(a) To verify: That the points ( 2 n π , 0 ) are asymptotically stable, while those at ( ( 2 n + 1 ) π , 0 ) are saddle points.

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Answer 1

Question

Chapter 12.4, Problem 21E

To determine

(a)

To verify:

That the points (2nπ,0) are asymptotically stable, while those at ((2n+1)π,0) are saddle points.

To determine

(b)

To verify:

That for b>2 the stable critical points are improper nodes, while for 0<b<2, these become spiral points

To determine

(c)

To describe:

The condition when b=2

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Answer 2

Question

Chapter 12.4, Problem 21E

To determine

(a)

To verify:

That the points (2nπ,0) are asymptotically stable, while those at ((2n+1)π,0) are saddle points.

To determine

(b)

To verify:

That for b>2 the stable critical points are improper nodes, while for 0<b<2, these become spiral points

To determine

(c)

To describe:

The condition when b=2

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 3

Question

Chapter 12.4, Problem 21E

To determine

(a)

To verify:

That the points (2nπ,0) are asymptotically stable, while those at ((2n+1)π,0) are saddle points.

To determine

(b)

To verify:

That for b>2 the stable critical points are improper nodes, while for 0<b<2, these become spiral points

To determine

(c)

To describe:

The condition when b=2

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 12.4, Problem 21E

To determine

(a)

To verify:

That the points (2nπ,0) are asymptotically stable, while those at ((2n+1)π,0) are saddle points.

To determine

(b)

To verify:

That for b>2 the stable critical points are improper nodes, while for 0<b<2, these become spiral points

To determine

(c)

To describe:

The condition when b=2

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 5

Chapter 12.4, Problem 21E

To determine

(a)

To verify:

That the points (2nπ,0) are asymptotically stable, while those at ((2n+1)π,0) are saddle points.

To determine

(b)

To verify:

That for b>2 the stable critical points are improper nodes, while for 0<b<2, these become spiral points

To determine

(c)

To describe:

The condition when b=2

Answer 6

Chapter 12.4, Problem 21E

To determine

(a)

To verify:

That the points (2nπ,0) are asymptotically stable, while those at ((2n+1)π,0) are saddle points.

Answer 7

Chapter 12.4, Problem 21E

To determine

(a)

To verify:

That the points (2nπ,0) are asymptotically stable, while those at ((2n+1)π,0) are saddle points.

Answer 8

To determine

(b)

To verify:

That for b>2 the stable critical points are improper nodes, while for 0<b<2, these become spiral points

Answer 9

To determine

(b)

To verify:

That for b>2 the stable critical points are improper nodes, while for 0<b<2, these become spiral points

Answer 10

To determine

(c)

To describe:

The condition when b=2

Answer 11

To determine

(c)

To describe:

The condition when b=2

Answer 12

Expert Solution & Answer

Answer 13

Expert Solution & Answer

Answer 14

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Answer 15

Ch. 12.2 - In Problem 16, classify the critical point at the...Ch. 12.2 - Prob. 2E Ch. 12.2 - Prob. 3E Ch. 12.2 - Prob. 4E Ch. 12.2 - Prob. 5E Ch. 12.2 - Prob. 6E Ch. 12.2 - Prob. 7E Ch. 12.2 - Prob. 8E Ch. 12.2 - Prob. 9E Ch. 12.2 - In Problem 712, find and classify the critical...

(a) To verify: That the points ( 2 n π , 0 ) are asymptotically stable, while those at ( ( 2 n + 1 ) π , 0 ) are saddle points.

Solution Summary: The author explains that the points are asymptotically stable, while those at (2n+1 )pi,0) are saddle points.

Concept explainers

Videos

(a)

To verify:

That the points (2nπ,0) are asymptotically stable, while those at ((2n+1)π,0) are saddle points.

(b)

To verify:

That for b>2 the stable critical points are improper nodes, while for 0<b<2, these become spiral points

(c)

To describe:

The condition when b=2

Want to see the full answer?

Chapter 12 Solutions

(a) To verify: That the points ( 2 n π , 0 ) are asymptotically stable, while those at ( ( 2 n + 1 ) π , 0 ) are saddle points.

Solution Summary: The author explains that the points are asymptotically stable, while those at (2n+1 )pi,0) are saddle points.

Concept explainers

Videos

(a) To verify: That the points (2nπ,0) are asymptotically stable, while those at ((2n+1)π,0) are saddle points.

(b) To verify: That for b>2 the stable critical points are improper nodes, while for 0<b<2, these become spiral points

(c) To describe: The condition when b=2

Want to see the full answer?

Chapter 12 Solutions

(a)

To verify:

That the points (2nπ,0) are asymptotically stable, while those at ((2n+1)π,0) are saddle points.

(b)

To verify:

That for b>2 the stable critical points are improper nodes, while for 0<b<2, these become spiral points

(c)

To describe:

The condition when b=2