(a) To sketch the slope field of the differential equation given in the range − 1 ≤ t ≤ 3 , − 1 ≤ y ≤ 3 by observing that the isoclines of slope c is in the line t − y = c , so the segments have slope c at points on the line y = t − c

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Answer 1

Question

Chapter 9.3, Problem 5E

To determine

(a)

To sketch the slope field of the differential equation given in the range −1≤t≤3,−1≤y≤3 by observing that the isoclines of slope c is in the line t−y=c, so the segments have slope c at points on the line y=t−c

To determine

(b)

To show that y=t−1+Ce−t is a solution for all C. Since limt→∞e−t=0 these solutions approach the particular solution y=t−1 as t→∞. Explain how this behavior is reflected in your slope field.

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Answer 2

Question

Chapter 9.3, Problem 5E

To determine

(a)

To sketch the slope field of the differential equation given in the range −1≤t≤3,−1≤y≤3 by observing that the isoclines of slope c is in the line t−y=c, so the segments have slope c at points on the line y=t−c

To determine

(b)

To show that y=t−1+Ce−t is a solution for all C. Since limt→∞e−t=0 these solutions approach the particular solution y=t−1 as t→∞. Explain how this behavior is reflected in your slope field.

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Answer 3

Question

Chapter 9.3, Problem 5E

To determine

(a)

To sketch the slope field of the differential equation given in the range −1≤t≤3,−1≤y≤3 by observing that the isoclines of slope c is in the line t−y=c, so the segments have slope c at points on the line y=t−c

To determine

(b)

To show that y=t−1+Ce−t is a solution for all C. Since limt→∞e−t=0 these solutions approach the particular solution y=t−1 as t→∞. Explain how this behavior is reflected in your slope field.

Expert Solution & Answer

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Answer 4

Question

Chapter 9.3, Problem 5E

To determine

(a)

To sketch the slope field of the differential equation given in the range −1≤t≤3,−1≤y≤3 by observing that the isoclines of slope c is in the line t−y=c, so the segments have slope c at points on the line y=t−c

To determine

(b)

To show that y=t−1+Ce−t is a solution for all C. Since limt→∞e−t=0 these solutions approach the particular solution y=t−1 as t→∞. Explain how this behavior is reflected in your slope field.

Expert Solution & Answer

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Answer 5

Chapter 9.3, Problem 5E

To determine

(a)

To sketch the slope field of the differential equation given in the range −1≤t≤3,−1≤y≤3 by observing that the isoclines of slope c is in the line t−y=c, so the segments have slope c at points on the line y=t−c

To determine

(b)

To show that y=t−1+Ce−t is a solution for all C. Since limt→∞e−t=0 these solutions approach the particular solution y=t−1 as t→∞. Explain how this behavior is reflected in your slope field.

Answer 6

Chapter 9.3, Problem 5E

To determine

(a)

To sketch the slope field of the differential equation given in the range −1≤t≤3,−1≤y≤3 by observing that the isoclines of slope c is in the line t−y=c, so the segments have slope c at points on the line y=t−c

Answer 7

Chapter 9.3, Problem 5E

To determine

(a)

To sketch the slope field of the differential equation given in the range −1≤t≤3,−1≤y≤3 by observing that the isoclines of slope c is in the line t−y=c, so the segments have slope c at points on the line y=t−c

Answer 8

To determine

(b)

To show that y=t−1+Ce−t is a solution for all C. Since limt→∞e−t=0 these solutions approach the particular solution y=t−1 as t→∞. Explain how this behavior is reflected in your slope field.

Answer 9

To determine

(b)

To show that y=t−1+Ce−t is a solution for all C. Since limt→∞e−t=0 these solutions approach the particular solution y=t−1 as t→∞. Explain how this behavior is reflected in your slope field.

Answer 10

Expert Solution & Answer

Answer 11

Expert Solution & Answer

Answer 12

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Answer 13

Ch. 9.1 - Prob. 1PQ Ch. 9.1 - Prob. 2PQ Ch. 9.1 - Prob. 3PQ Ch. 9.1 - Prob. 4PQ Ch. 9.1 - Prob. 1E Ch. 9.1 - Prob. 2E Ch. 9.1 - Prob. 3E Ch. 9.1 - Prob. 4E Ch. 9.1 - Prob. 5E Ch. 9.1 - Prob. 6E

(a) To sketch the slope field of the differential equation given in the range − 1 ≤ t ≤ 3 , − 1 ≤ y ≤ 3 by observing that the isoclines of slope c is in the line t − y = c , so the segments have slope c at points on the line y = t − c

Solution Summary: The author illustrates how the slope field of the differential equation is sketched by observing that the isoclines of slope c are in the line.

Concept explainers

Videos

(a)

To sketch the slope field of the differential equation given in the range −1≤t≤3,−1≤y≤3 by observing that the isoclines of slope c is in the line t−y=c, so the segments have slope c at points on the line y=t−c

(b)

To show that y=t−1+Ce−t is a solution for all C. Since limt→∞e−t=0 these solutions approach the particular solution y=t−1 as t→∞. Explain how this behavior is reflected in your slope field.

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Chapter 9 Solutions

(a) To sketch the slope field of the differential equation given in the range − 1 ≤ t ≤ 3 , − 1 ≤ y ≤ 3 by observing that the isoclines of slope c is in the line t − y = c , so the segments have slope c at points on the line y = t − c

Solution Summary: The author illustrates how the slope field of the differential equation is sketched by observing that the isoclines of slope c are in the line.

Concept explainers

Videos

(a) To sketch the slope field of the differential equation given in the range −1≤t≤3,−1≤y≤3 by observing that the isoclines of slope c is in the line t−y=c, so the segments have slope c at points on the line y=t−c

(b) To show that y=t−1+Ce−t is a solution for all C. Since limt→∞e−t=0 these solutions approach the particular solution y=t−1 as t→∞. Explain how this behavior is reflected in your slope field.

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Chapter 9 Solutions

(a)

To sketch the slope field of the differential equation given in the range −1≤t≤3,−1≤y≤3 by observing that the isoclines of slope c is in the line t−y=c, so the segments have slope c at points on the line y=t−c

(b)

To show that y=t−1+Ce−t is a solution for all C. Since limt→∞e−t=0 these solutions approach the particular solution y=t−1 as t→∞. Explain how this behavior is reflected in your slope field.