The given equationis to be fixedfora finite time x ( t ) → ± ∞ , where r > 0 Concept Introduction: By using the concept of existence and uniqueness the solution of the given equation x ˙ = rx+x 3 where r > 0 , is found out. The existence and uniqueness theorem says that, ‘ f(x) , and f'(x) are continuous on an open interval R of the x-axis, and suppose that x 0 is a point in R. Then the initial value problem has a solution x(t) on some time interval (-t,t) about t = 0 , and the solution is unique’.

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Answer 1

Question

Chapter 2.5, Problem 3E

Interpretation Introduction

Interpretation:

The given equationis to be fixedfora finite time x(t)→±∞, where r > 0

Concept Introduction:

By using the concept of existence and uniqueness the solution of the given equation x˙ = rx+x3 where r > 0, is found out.

The existence and uniqueness theorem says that, ‘f(x), and f'(x) are continuous on an open interval R of the x-axis, and suppose that x0 is a point in R. Then the initial value problem has a solution x(t) on some time interval (-t,t) about t = 0, and the solution is unique’.

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Answer 2

Question

Chapter 2.5, Problem 3E

Interpretation Introduction

Interpretation:

The given equationis to be fixedfora finite time x(t)→±∞, where r > 0

Concept Introduction:

By using the concept of existence and uniqueness the solution of the given equation x˙ = rx+x3 where r > 0, is found out.

The existence and uniqueness theorem says that, ‘f(x), and f'(x) are continuous on an open interval R of the x-axis, and suppose that x0 is a point in R. Then the initial value problem has a solution x(t) on some time interval (-t,t) about t = 0, and the solution is unique’.

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Check out a sample textbook solution

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Answer 3

Question

Chapter 2.5, Problem 3E

Interpretation Introduction

Interpretation:

The given equationis to be fixedfora finite time x(t)→±∞, where r > 0

Concept Introduction:

By using the concept of existence and uniqueness the solution of the given equation x˙ = rx+x3 where r > 0, is found out.

The existence and uniqueness theorem says that, ‘f(x), and f'(x) are continuous on an open interval R of the x-axis, and suppose that x0 is a point in R. Then the initial value problem has a solution x(t) on some time interval (-t,t) about t = 0, and the solution is unique’.

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Answer 4

Question

Chapter 2.5, Problem 3E

Interpretation Introduction

Interpretation:

The given equationis to be fixedfora finite time x(t)→±∞, where r > 0

Concept Introduction:

By using the concept of existence and uniqueness the solution of the given equation x˙ = rx+x3 where r > 0, is found out.

The existence and uniqueness theorem says that, ‘f(x), and f'(x) are continuous on an open interval R of the x-axis, and suppose that x0 is a point in R. Then the initial value problem has a solution x(t) on some time interval (-t,t) about t = 0, and the solution is unique’.

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Answer 5

Chapter 2.5, Problem 3E

Interpretation Introduction

Interpretation:

The given equationis to be fixedfora finite time x(t)→±∞, where r > 0

Concept Introduction:

By using the concept of existence and uniqueness the solution of the given equation x˙ = rx+x3 where r > 0, is found out.

The existence and uniqueness theorem says that, ‘f(x), and f'(x) are continuous on an open interval R of the x-axis, and suppose that x0 is a point in R. Then the initial value problem has a solution x(t) on some time interval (-t,t) about t = 0, and the solution is unique’.

Answer 6

Chapter 2.5, Problem 3E

Interpretation Introduction

Interpretation:

The given equationis to be fixedfora finite time x(t)→±∞, where r > 0

Concept Introduction:

By using the concept of existence and uniqueness the solution of the given equation x˙ = rx+x3 where r > 0, is found out.

The existence and uniqueness theorem says that, ‘f(x), and f'(x) are continuous on an open interval R of the x-axis, and suppose that x0 is a point in R. Then the initial value problem has a solution x(t) on some time interval (-t,t) about t = 0, and the solution is unique’.

Answer 7

Chapter 2.5, Problem 3E

Interpretation Introduction

Interpretation:

The given equationis to be fixedfora finite time x(t)→±∞, where r > 0

Concept Introduction:

By using the concept of existence and uniqueness the solution of the given equation x˙ = rx+x3 where r > 0, is found out.

The existence and uniqueness theorem says that, ‘f(x), and f'(x) are continuous on an open interval R of the x-axis, and suppose that x0 is a point in R. Then the initial value problem has a solution x(t) on some time interval (-t,t) about t = 0, and the solution is unique’.

Answer 8

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Answer 9

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Answer 10

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Answer 11

Ch. 2.1 - Prob. 1E Ch. 2.1 - Prob. 2E Ch. 2.1 - Prob. 3E Ch. 2.1 - Prob. 4E Ch. 2.1 - Prob. 5E Ch. 2.2 - Prob. 1E Ch. 2.2 - Prob. 2E Ch. 2.2 - Prob. 3E Ch. 2.2 - Prob. 4E Ch. 2.2 - Prob. 5E

Solution Summary: The author explains the existence and uniqueness theorem for the given equation by integrating and rearranging the terms.

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