To show that x ˙ = − x + 2 y 3 − 2 y 4 , y ˙ = − x − y + x y has no periodic solutions. Concept Introduction: Positive definiteis a continuously differentiable real value function V(x,y) . The function V(x,y) can be represented as V=x m +ay n if the power term of the function is even.

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Answer 1

Question

Chapter 7.2, Problem 12E

Interpretation Introduction

Interpretation:

To show that x˙=−x+2y3−2y4, y˙=−x−y+xy has no periodic solutions.

Concept Introduction:

Positive definiteis a continuously differentiable real value function V(x,y).

The function V(x,y) can be represented as V=xm+ayn if the power term of the function is even.

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2. Let m(x) = 2x² - ax - 2 and n(x) = bx² + 2x + 5. The functions are combined to form the new function p(x) = m(x)n(x). Points (1,-40) and (-1, 24) satisfy the new function. Determine m(x) and n(x). Leave the final answer in exact form.

Let (-1, (-1) = 2), (0, ƒ(0) = 5) and (1, f(1) = 6). Which one gives quadratic spline functions? (Choose by = 2) %3D Select one: .-5x +x + 5,-1 5 x <0 and x + 5,0 s x S 1 O b. None of them O C. -x + 2x + 5,-1 Sx <0 and -x + 2x + 5,0 sx< 1 O d. -5x + 2x + 5,-1 s x < 0 and x + 5,0 < x < 1 O e.x² +2x + 5,-1 5 x 5 0 and x² + 2x + 5.0 < xs 1 e. X

1. The functions fi(x) = 4x, f2(x) = x² + 6x, and fз(x) = 4x² + 12x do not form a linearly independent set of functions. Verify this by writing one of the given functions as a linear combination of the other two functions. (4 pts.)

Answer 2

Question

Chapter 7.2, Problem 12E

Interpretation Introduction

Interpretation:

To show that x˙=−x+2y3−2y4, y˙=−x−y+xy has no periodic solutions.

Concept Introduction:

Positive definiteis a continuously differentiable real value function V(x,y).

The function V(x,y) can be represented as V=xm+ayn if the power term of the function is even.

Expert Solution & Answer

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Answer 3

Question

Chapter 7.2, Problem 12E

Interpretation Introduction

Interpretation:

To show that x˙=−x+2y3−2y4, y˙=−x−y+xy has no periodic solutions.

Concept Introduction:

Positive definiteis a continuously differentiable real value function V(x,y).

The function V(x,y) can be represented as V=xm+ayn if the power term of the function is even.

Expert Solution & Answer

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Answer 4

Question

Chapter 7.2, Problem 12E

Interpretation Introduction

Interpretation:

To show that x˙=−x+2y3−2y4, y˙=−x−y+xy has no periodic solutions.

Concept Introduction:

Positive definiteis a continuously differentiable real value function V(x,y).

The function V(x,y) can be represented as V=xm+ayn if the power term of the function is even.

Expert Solution & Answer

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See solution

Answer 5

Chapter 7.2, Problem 12E

Interpretation Introduction

Interpretation:

To show that x˙=−x+2y3−2y4, y˙=−x−y+xy has no periodic solutions.

Concept Introduction:

Positive definiteis a continuously differentiable real value function V(x,y).

The function V(x,y) can be represented as V=xm+ayn if the power term of the function is even.

Answer 6

Chapter 7.2, Problem 12E

Interpretation Introduction

Interpretation:

To show that x˙=−x+2y3−2y4, y˙=−x−y+xy has no periodic solutions.

Concept Introduction:

Positive definiteis a continuously differentiable real value function V(x,y).

The function V(x,y) can be represented as V=xm+ayn if the power term of the function is even.

Answer 7

Chapter 7.2, Problem 12E

Interpretation Introduction

Interpretation:

To show that x˙=−x+2y3−2y4, y˙=−x−y+xy has no periodic solutions.

Concept Introduction:

Positive definiteis a continuously differentiable real value function V(x,y).

The function V(x,y) can be represented as V=xm+ayn if the power term of the function is even.

Answer 8

Expert Solution & Answer

Answer 9

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Answer 10

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Answer 11

Ch. 7.1 - Prob. 1E Ch. 7.1 - Prob. 2E Ch. 7.1 - Prob. 3E Ch. 7.1 - Prob. 4E Ch. 7.1 - Prob. 5E Ch. 7.1 - Prob. 6E Ch. 7.1 - Prob. 7E Ch. 7.1 - Prob. 8E Ch. 7.1 - Prob. 9E Ch. 7.2 - Prob. 1E

To show that x ˙ = − x + 2 y 3 − 2 y 4 , y ˙ = − x − y + x y has no periodic solutions. Concept Introduction: Positive definiteis a continuously differentiable real value function V(x,y) . The function V(x,y) can be represented as V=x m +ay n if the power term of the function is even.

Solution Summary: The author explains that positive definite is a continuously differentiable real value function V(x,y).

Concept explainers

Videos

Interpretation:

To show that x˙=−x+2y3−2y4, y˙=−x−y+xy has no periodic solutions.

Concept Introduction:

Positive definiteis a continuously differentiable real value function V(x,y).

The function V(x,y) can be represented as V=xm+ayn if the power term of the function is even.

Want to see the full answer?

Chapter 7 Solutions

To show that x ˙ = − x + 2 y 3 − 2 y 4 , y ˙ = − x − y + x y has no periodic solutions. Concept Introduction: Positive definiteis a continuously differentiable real value function V(x,y) . The function V(x,y) can be represented as V=x m +ay n if the power term of the function is even.

Solution Summary: The author explains that positive definite is a continuously differentiable real value function V(x,y).

Concept explainers

Videos

Interpretation: To show that x˙=−x+2y3−2y4, y˙=−x−y+xy has no periodic solutions. Concept Introduction: Positive definiteis a continuously differentiable real value function V(x,y). The function V(x,y) can be represented as V=xm+ayn if the power term of the function is even.

Want to see the full answer?

Chapter 7 Solutions

Interpretation:

To show that x˙=−x+2y3−2y4, y˙=−x−y+xy has no periodic solutions.

Concept Introduction:

Positive definiteis a continuously differentiable real value function V(x,y).

The function V(x,y) can be represented as V=xm+ayn if the power term of the function is even.