(a) To find: The direction field in the phase plane for the system d x / d t = y , d y / d t = − x + x 3 . and check whether the solution passing through the point ( 0.25 , 0.25 ) is periodic or not.

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Answer 1

Question

Chapter 5.4, Problem 25E

To determine

(a)

To find:

The direction field in the phase plane for the system

dx/dt=y,

dy/dt=−x+x3.

and check whether the solution passing through the point (0.25,0.25) is periodic or not.

To determine

(b)

To find:

Whether the solution passing through the point (2,2) is periodic or not.

To determine

(c)

To find:

Whether the solution passing through the point (1,0) is periodic or not.

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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 5.4, Problem 25E

To determine

(a)

To find:

The direction field in the phase plane for the system

dx/dt=y,

dy/dt=−x+x3.

and check whether the solution passing through the point (0.25,0.25) is periodic or not.

To determine

(b)

To find:

Whether the solution passing through the point (2,2) is periodic or not.

To determine

(c)

To find:

Whether the solution passing through the point (1,0) is periodic or not.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 3

Question

Chapter 5.4, Problem 25E

To determine

(a)

To find:

The direction field in the phase plane for the system

dx/dt=y,

dy/dt=−x+x3.

and check whether the solution passing through the point (0.25,0.25) is periodic or not.

To determine

(b)

To find:

Whether the solution passing through the point (2,2) is periodic or not.

To determine

(c)

To find:

Whether the solution passing through the point (1,0) is periodic or not.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 5.4, Problem 25E

To determine

(a)

To find:

The direction field in the phase plane for the system

dx/dt=y,

dy/dt=−x+x3.

and check whether the solution passing through the point (0.25,0.25) is periodic or not.

To determine

(b)

To find:

Whether the solution passing through the point (2,2) is periodic or not.

To determine

(c)

To find:

Whether the solution passing through the point (1,0) is periodic or not.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 5

Chapter 5.4, Problem 25E

To determine

(a)

To find:

The direction field in the phase plane for the system

dx/dt=y,

dy/dt=−x+x3.

and check whether the solution passing through the point (0.25,0.25) is periodic or not.

To determine

(b)

To find:

Whether the solution passing through the point (2,2) is periodic or not.

To determine

(c)

To find:

Whether the solution passing through the point (1,0) is periodic or not.

Answer 6

Chapter 5.4, Problem 25E

To determine

(a)

To find:

The direction field in the phase plane for the system

dx/dt=y,

dy/dt=−x+x3.

and check whether the solution passing through the point (0.25,0.25) is periodic or not.

Answer 7

Chapter 5.4, Problem 25E

To determine

(a)

To find:

The direction field in the phase plane for the system

dx/dt=y,

dy/dt=−x+x3.

and check whether the solution passing through the point (0.25,0.25) is periodic or not.

Answer 8

To determine

(b)

To find:

Whether the solution passing through the point (2,2) is periodic or not.

Answer 9

To determine

(b)

To find:

Whether the solution passing through the point (2,2) is periodic or not.

Answer 10

To determine

(c)

To find:

Whether the solution passing through the point (1,0) is periodic or not.

Answer 11

To determine

(c)

To find:

Whether the solution passing through the point (1,0) is periodic or not.

Answer 12

Expert Solution & Answer

Answer 13

Expert Solution & Answer

Answer 14

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Answer 15

(a) To find: The direction field in the phase plane for the system d x / d t = y , d y / d t = − x + x 3 . and check whether the solution passing through the point ( 0.25 , 0.25 ) is periodic or not.

Solution Summary: The author explains how to find the direction field in the phase plane for the system dx/dt=y.

Concept explainers

Videos

(a)

To find:

The direction field in the phase plane for the system

dx/dt=y,

dy/dt=−x+x3.

and check whether the solution passing through the point (0.25,0.25) is periodic or not.

(b)

To find:

Whether the solution passing through the point (2,2) is periodic or not.

(c)

To find:

Whether the solution passing through the point (1,0) is periodic or not.

Want to see the full answer?

Chapter 5 Solutions

(a) To find: The direction field in the phase plane for the system d x / d t = y , d y / d t = − x + x 3 . and check whether the solution passing through the point ( 0.25 , 0.25 ) is periodic or not.

Solution Summary: The author explains how to find the direction field in the phase plane for the system dx/dt=y.

Concept explainers

Videos

(a) To find: The direction field in the phase plane for the system dx/dt=y, dy/dt=−x+x3. and check whether the solution passing through the point (0.25,0.25) is periodic or not.

(b) To find: Whether the solution passing through the point (2,2) is periodic or not.

(c) To find: Whether the solution passing through the point (1,0) is periodic or not.

Want to see the full answer?

Chapter 5 Solutions

(a)

To find:

The direction field in the phase plane for the system

dx/dt=y,

dy/dt=−x+x3.

and check whether the solution passing through the point (0.25,0.25) is periodic or not.

(b)

To find:

Whether the solution passing through the point (2,2) is periodic or not.

(c)

To find:

Whether the solution passing through the point (1,0) is periodic or not.