EBK DIFFERENTIAL EQUATIONS AND LINEAR A
4th Edition
ISBN: 8220102019799
Author: ANNIN
Publisher: YUZU
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Textbook Question
Chapter 10.10, Problem 34AP
For Problems 34-40, use the Laplace transform to solve the given initial-value problem.
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1. A hot metal object is submerged in a large tank of water held at temperature 25° C.
Let y(t) be the temperature of the object t minutes after it is submerged in water.
Newton's Law of Cooling says that the temperature will change according to
dy
-2(y – 25).
dt
Suppose the object was 150°C before submerging it in water. Find the function y(t).
Do not present a solution based on a formula that you might be able to look up, show your own work
here.
For Problems 12 and 14, use the Laplace transform to solve the given initialvalue problem.
The correct answer for 12: 10 te^(-5t)
The correct answer for 14: -(1/2)sint + 2cost - (1/2)tcost. Please show how to get the correct answer for 12 and 14. thank you
Example 10.8. Using Euler's method, find an approximate value of y corresponding to
x= 1, given that dy/dx = x +y and y= 1 when x = 0.
Chapter 10 Solutions
EBK DIFFERENTIAL EQUATIONS AND LINEAR A
Ch. 10.1 - For Questions a-i, decide if the given statement...Ch. 10.1 - For Questions a-i, decide if the given statement...Ch. 10.1 - For Questions a-i, decide if the given statement...Ch. 10.1 - For Questions a-i, decide if the given statement...Ch. 10.1 - For Questions a-i, decide if the given statement...Ch. 10.1 - For Questions a-i, decide if the given statement...Ch. 10.1 - Prob. 7TFRCh. 10.1 - For Questions a-i, decide if the given statement...Ch. 10.1 - For Questions a-i, decide if the given statement...Ch. 10.1 - Problems For Problems 1-12, use 10.1.1 to...
Ch. 10.1 - Problems For Problems 1-12, use 10.1.1 to...Ch. 10.1 - Problems For Problems 1-12, use 10.1.1 to...Ch. 10.1 - Problems For Problems 1-12, use 10.1.1 to...Ch. 10.1 - Problems For Problems 1-12, use 10.1.1 to...Ch. 10.1 - Prob. 6PCh. 10.1 - Problems For Problems 1-12, use 10.1.1 to...Ch. 10.1 - Prob. 8PCh. 10.1 - Problems For Problems 1-12, use 10.1.1 to...Ch. 10.1 - Prob. 10PCh. 10.1 - Problems For Problems 1-12, use 10.1.1 to...Ch. 10.1 - Prob. 12PCh. 10.1 - Problems For Problems 13-22, use the linearity of...Ch. 10.1 - Prob. 14PCh. 10.1 - Problems For Problems 13-22, use the linearity of...Ch. 10.1 - PROBLEMNS For Problems 13-22, use the linearity of...Ch. 10.1 - Prob. 17PCh. 10.1 - PROBLEMNS For Problems 13-22, use the linearity of...Ch. 10.1 - PROBLEMNS For Problems 13-22, use the linearity of...Ch. 10.1 - PROBLEMNS For Problems 13-22, use the linearity of...Ch. 10.1 - PROBLEMNS For Problems 13-22, use the linearity of...Ch. 10.1 - PROBLEMNS For Problems 13-22, use the linearity of...Ch. 10.1 - PROBLEMNS For Problems 23-30, sketch the given...Ch. 10.1 - Prob. 24PCh. 10.1 - PROBLEMNS For Problems 23-30, sketch the given...Ch. 10.1 - Prob. 26PCh. 10.1 - For Problems 23-30, sketch the given function and...Ch. 10.1 - For Problems 23-30, sketch the given function and...Ch. 10.1 - For Problems 23-30, sketch the given function and...Ch. 10.1 - For Problems 23-30, sketch the given function and...Ch. 10.1 - For Problems 31-34, sketch the given function and...Ch. 10.1 - For Problems 31-34, sketch the given function and...Ch. 10.1 - For Problems 31-34, sketch the given function and...Ch. 10.1 - Prob. 34PCh. 10.1 - Prob. 35PCh. 10.1 - Prob. 36PCh. 10.1 - Use mathematical induction to prove that for every...Ch. 10.1 - Prob. 38PCh. 10.2 - True-False Review For Questions (a)-(f) decide if...Ch. 10.2 - True-False Review For Questions (a)-(f) decide if...Ch. 10.2 - Prob. 3TFRCh. 10.2 - Prob. 4TFRCh. 10.2 - Prob. 5TFRCh. 10.2 - Prob. 6TFRCh. 10.2 - Prob. 1PCh. 10.2 - Prob. 2PCh. 10.2 - Prob. 3PCh. 10.2 - Prob. 4PCh. 10.2 - For Problem 1-5, show that the given function is...Ch. 10.2 - Prob. 6PCh. 10.2 - Prob. 7PCh. 10.2 - For Problem 7-21, determine the inverse Laplace...Ch. 10.2 - For Problem 7-21, determine the inverse Laplace...Ch. 10.2 - For Problem 7-21, determine the inverse Laplace...Ch. 10.2 - For Problem 7-21, determine the inverse Laplace...Ch. 10.2 - For Problem 7-21, determine the inverse Laplace...Ch. 10.2 - For Problem 7-21, determine the inverse Laplace...Ch. 10.2 - Prob. 14PCh. 10.2 - For Problem 7-21, determine the inverse Laplace...Ch. 10.2 - Prob. 16PCh. 10.2 - For Problem 7-21, determine the inverse Laplace...Ch. 10.2 - For Problem 7-21, determine the inverse Laplace...Ch. 10.2 - For Problem 7-21, determine the inverse Laplace...Ch. 10.2 - For Problem 7-21, determine the inverse Laplace...Ch. 10.2 - Problems For Problem 7-21, determine the inverse...Ch. 10.2 - Prob. 22PCh. 10.3 - For Questions (a)-(h) decide if the given...Ch. 10.3 - Prob. 2TFRCh. 10.3 - Prob. 3TFRCh. 10.3 - Prob. 4TFRCh. 10.3 - Prob. 5TFRCh. 10.3 - Prob. 6TFRCh. 10.3 - True-False Review For Questions (a)-(h) decide if...Ch. 10.3 - Problems For Problems 1-9, determine the Laplace...Ch. 10.3 - Prob. 2PCh. 10.3 - Problems For Problem 1-9, determine the Laplace...Ch. 10.3 - Prob. 4PCh. 10.3 - Problems For Problem 1-9, determine the Laplace...Ch. 10.3 - Prob. 6PCh. 10.3 - Problems For Problem 1-9, determine the Laplace...Ch. 10.3 - Prob. 8PCh. 10.3 - Problems For Problem 1-9, determine the Laplace...Ch. 10.3 - Prob. 10PCh. 10.3 - Prob. 11PCh. 10.4 - For Questions a-d, decide if the given statement...Ch. 10.4 - Prob. 2TFRCh. 10.4 - Prob. 3TFRCh. 10.4 - Prob. 4TFRCh. 10.4 - Problems For problem 1-27, use the Laplace...Ch. 10.4 - Problems For problems 1-27, use the Laplace...Ch. 10.4 - Problems For problem 1-27, use the Laplace...Ch. 10.4 - Problems For problem 1-27, use the Laplace...Ch. 10.4 - Problems For problem 1-27, use the Laplace...Ch. 10.4 - Prob. 6PCh. 10.4 - Problems For problem 1-27, use the Laplace...Ch. 10.4 - Problems For problem 1-27, use the Laplace...Ch. 10.4 - Problems For problem 1-27, use the Laplace...Ch. 10.4 - Problems For problem 1-27, use the Laplace...Ch. 10.4 - Problems For problem 1-27, use the Laplace...Ch. 10.4 - Problems For problem 1-27, use the Laplace...Ch. 10.4 - Problems For problems 1-27, use the Laplace...Ch. 10.4 - Prob. 14PCh. 10.4 - Problems For problem 1-27, use the Laplace...Ch. 10.4 - Problems For problem 1-27, use the Laplace...Ch. 10.4 - Problems For problem 1-27, use the Laplace...Ch. 10.4 - Problems For problem 1-27, use the Laplace...Ch. 10.4 - Prob. 19PCh. 10.4 - Problems For problem 1-27, use the Laplace...Ch. 10.4 - Prob. 21PCh. 10.4 - Prob. 22PCh. 10.4 - Prob. 23PCh. 10.4 - Prob. 24PCh. 10.4 - Problems For problem 1-27, use the Laplace...Ch. 10.4 - Prob. 26PCh. 10.4 - Problems For problem 1-27, use the Laplace...Ch. 10.4 - Prob. 28PCh. 10.4 - Prob. 29PCh. 10.4 - Prob. 30PCh. 10.4 - Prob. 31PCh. 10.4 - Prob. 32PCh. 10.4 - Prob. 34PCh. 10.5 - True-False Review For Questions (a)(h), decide if...Ch. 10.5 - Prob. 2TFRCh. 10.5 - True-False Review For Questions (a)(h), decide if...Ch. 10.5 - Prob. 4TFRCh. 10.5 - Prob. 5TFRCh. 10.5 - Prob. 6TFRCh. 10.5 - Prob. 7TFRCh. 10.5 - Prob. 8TFRCh. 10.5 - For Problems 1-11, determine f(ta) for the given...Ch. 10.5 - Prob. 2PCh. 10.5 - Prob. 3PCh. 10.5 - Prob. 4PCh. 10.5 - For Problems 1-11, determine f(ta) for the given...Ch. 10.5 - Prob. 6PCh. 10.5 - Prob. 7PCh. 10.5 - Prob. 8PCh. 10.5 - Prob. 9PCh. 10.5 - Prob. 10PCh. 10.5 - Prob. 11PCh. 10.5 - Prob. 12PCh. 10.5 - For Problems 12-17, determine f(t). f(t1)=(t2)2.Ch. 10.5 - Prob. 14PCh. 10.5 - For Problems 12-17, determine f(t)....Ch. 10.5 - Prob. 16PCh. 10.5 - Prob. 17PCh. 10.5 - For Problems 18-27, determine the Laplace...Ch. 10.5 - For Problems 18-27, determine the Laplace...Ch. 10.5 - For Problems 18-27, determine the Laplace...Ch. 10.5 - For Problems 18-27, determine the Laplace...Ch. 10.5 - For Problems 18-27, determine the Laplace...Ch. 10.5 - Prob. 23PCh. 10.5 - For Problems 18-27, determine the Laplace...Ch. 10.5 - For Problems 18-27, determine the Laplace...Ch. 10.5 - Prob. 26PCh. 10.5 - For Problems 18-27, determine the Laplace...Ch. 10.5 - Prob. 28PCh. 10.5 - For Problems 28-42, determine L1[F]. F(s)=4(s+2)3.Ch. 10.5 - Prob. 30PCh. 10.5 - For Problems 28-42, determine L1[F]....Ch. 10.5 - Prob. 32PCh. 10.5 - For Problems 28-42, determine L1[F]....Ch. 10.5 - Prob. 34PCh. 10.5 - Prob. 35PCh. 10.5 - Prob. 36PCh. 10.5 - For Problems 28-42, determine L1[F]....Ch. 10.5 - Prob. 38PCh. 10.5 - For Problems 28-42, determine L1[F]....Ch. 10.5 - Prob. 40PCh. 10.5 - For Problems 28-42, determine L1[F]....Ch. 10.5 - Prob. 42PCh. 10.5 - For Problems 43-53, solve the given initial-value...Ch. 10.5 - Prob. 44PCh. 10.5 - For Problems 43-53, solve the given initial-value...Ch. 10.5 - Prob. 46PCh. 10.5 - For Problems 43-53, solve the given initial-value...Ch. 10.5 - For Problems 43-53, solve the given initial-value...Ch. 10.5 - For Problems 43-53, solve the given initial-value...Ch. 10.5 - Prob. 50PCh. 10.5 - Prob. 51PCh. 10.5 - For Problems 43-53, solve the given initial-value...Ch. 10.5 - For Problems 43-53, solve the given initial-value...Ch. 10.5 - Prob. 54PCh. 10.5 - Prob. 55PCh. 10.6 - For Questions a-d, decide if the given statement...Ch. 10.6 - For Questions a-d, decide if the given statement...Ch. 10.6 - Prob. 3TFRCh. 10.6 - Prob. 4TFRCh. 10.6 - Problems: For Problems 1-7, make a sketch of the...Ch. 10.6 - Problems: For Problems 1-7, make a sketch of the...Ch. 10.6 - Problems: For Problems 1-7, make a sketch of the...Ch. 10.6 - Problems: For Problems 1-7, make a sketch of the...Ch. 10.6 - Problems: For Problems 1-7, make a sketch of the...Ch. 10.6 - Prob. 6PCh. 10.6 - Prob. 7PCh. 10.6 - Problems: For Problems 8-15, make a sketch of the...Ch. 10.6 - Problems: For Problems 8-15, make a sketch of the...Ch. 10.6 - Problems: For Problems 8-15, make a sketch of the...Ch. 10.6 - Problems: For Problems 8-15, make a sketch of the...Ch. 10.6 - Problems: For Problems 8-15, make a sketch of the...Ch. 10.6 - Problems: For Problems 8-15, make a sketch of the...Ch. 10.6 - Problems: For Problems 8-15, make a sketch of the...Ch. 10.6 - Prob. 15PCh. 10.7 - True-False Review For Questions (a)(g), decide if...Ch. 10.7 - Prob. 2TFRCh. 10.7 - Prob. 3TFRCh. 10.7 - Prob. 4TFRCh. 10.7 - Prob. 5TFRCh. 10.7 - Prob. 7TFRCh. 10.7 - Problems
For Problems 1-11, determine the...Ch. 10.7 - Problems
For Problems 1-11, determine the...Ch. 10.7 - Problems
For Problems 1-11, determine the...Ch. 10.7 - Problems
For Problems 1-11, determine the...Ch. 10.7 - Problems
For Problems 1-11, determine the...Ch. 10.7 - Problems
For Problems 1-11, determine the...Ch. 10.7 - Problems
For Problems 1-11, determine the...Ch. 10.7 - Problems
For Problems 1-11, determine the...Ch. 10.7 - Problems
For Problems 1-11, determine the...Ch. 10.7 - Prob. 10PCh. 10.7 - Problems
For Problems 1-11, determine the...Ch. 10.7 - Problems
For Problems 12-26, determine the...Ch. 10.7 - Problems
For Problems 12-26, determine the...Ch. 10.7 - Prob. 14PCh. 10.7 - Problems
For Problems 12-26, determine the...Ch. 10.7 - Prob. 16PCh. 10.7 - Problems
For Problems 12-26, determine the...Ch. 10.7 - Prob. 18PCh. 10.7 - Problems
For Problems 12-26, determine the...Ch. 10.7 - Prob. 20PCh. 10.7 - Problems
For Problems 12-26, determine the...Ch. 10.7 - Prob. 22PCh. 10.7 - Prob. 23PCh. 10.7 - Prob. 24PCh. 10.7 - Problems
For Problems 12-26, determine the...Ch. 10.7 - Prob. 26PCh. 10.7 - For Problems 27-41, solve the given initial-value...Ch. 10.7 - Prob. 28PCh. 10.7 - Prob. 29PCh. 10.7 - Prob. 30PCh. 10.7 - Prob. 31PCh. 10.7 - Problems For Problems 27-41, solve the given...Ch. 10.7 - For Problems 27-41, solve the given initial-value...Ch. 10.7 - For Problems 27-41, solve the given initial-value...Ch. 10.7 - For Problems 27-41, solve the given initial-value...Ch. 10.7 - Prob. 36PCh. 10.7 - Prob. 37PCh. 10.7 - Problems For Problems 27-41, solve the given...Ch. 10.7 - Prob. 39PCh. 10.7 - Problems For Problems 27-41, solve the given...Ch. 10.7 - Prob. 41PCh. 10.7 - Problems For Problems 42-45, solve the given...Ch. 10.7 - For Problems 4245, solve the given initial value...Ch. 10.7 - Prob. 48PCh. 10.8 - For Questions a-d, decide if the given statement...Ch. 10.8 - For Questions a-d, decide if the given statement...Ch. 10.8 - Prob. 3TFRCh. 10.8 - Prob. 4TFRCh. 10.8 - Prob. 5TFRCh. 10.8 - For Problem 1-13, solve the given initial value...Ch. 10.8 - For Problem 1-13, solve the given initial value...Ch. 10.8 - For Problem 1-13, solve the given initial value...Ch. 10.8 - Prob. 4PCh. 10.8 - For Problem 1-13, solve the given initial value...Ch. 10.8 - Prob. 6PCh. 10.8 - For Problem 1-13, solve the given initial value...Ch. 10.8 - Prob. 8PCh. 10.8 - For Problem 1-13, solve the given initial value...Ch. 10.8 - Prob. 10PCh. 10.8 - Prob. 11PCh. 10.8 - Prob. 12PCh. 10.8 - For Problems 1-13, solve the given initial value...Ch. 10.8 - The motion of a spring-mass system is governed by...Ch. 10.8 - Prob. 15PCh. 10.8 - Prob. 16PCh. 10.9 - True-False Review For Questions (a)(g), decide if...Ch. 10.9 - Prob. 2TFRCh. 10.9 - True-False Review For Questions (a)(g), decide if...Ch. 10.9 - True-False Review For Questions (a)(g), decide if...Ch. 10.9 - Prob. 6TFRCh. 10.9 - Prob. 7TFRCh. 10.9 - Problems For Problems 1-6, determine fg. f(t)=t,...Ch. 10.9 - Problems For Problems 1-6, determine fg. f(t)=6t2,...Ch. 10.9 - Prob. 3PCh. 10.9 - Problems For Problems 1-6, determine fg. f(t)=et,...Ch. 10.9 - Problems For Problems 1-6, determine fg. f(t)=t2,...Ch. 10.9 - Problems For Problems 1-6, determine fg. f(t)=et,...Ch. 10.9 - Problems Prove that fg=gf.Ch. 10.9 - Problems Prove that f(gh)=(fg)h.Ch. 10.9 - Problems Prove that f(g+h)=(fg)+(fh).Ch. 10.9 - Problems For Problems 10-14, determine L(fg)....Ch. 10.9 - Problems For Problems 10-14, determine L(fg)....Ch. 10.9 - Problems For Problems 10-14, determine L(fg)....Ch. 10.9 - Problems For Problems 10-14, determine L(fg)....Ch. 10.9 - Prob. 14PCh. 10.9 - Problems For Problems 15-20, determine...Ch. 10.9 - Problems For Problems 15-20, determine...Ch. 10.9 - Prob. 17PCh. 10.9 - Prob. 18PCh. 10.9 - Prob. 19PCh. 10.9 - Prob. 21PCh. 10.9 - Problems For Problems 21-25, express L1[F(s)G(s)]...Ch. 10.9 - Problems For Problems 21-25, express L1[F(s)G(s)]...Ch. 10.9 - Prob. 24PCh. 10.9 - Problems For Problems 21-25, express L1[F(s)G(s)]...Ch. 10.9 - Prob. 26PCh. 10.9 - Problems Problems 26-32, solve the given...Ch. 10.9 - Problems Problems 26-32, solve the given...Ch. 10.9 - Problems Problems 26-32, solve the given...Ch. 10.9 - Problems Problems 26-32, solve the given...Ch. 10.9 - Prob. 31PCh. 10.9 - Prob. 32PCh. 10.9 - Prob. 33PCh. 10.9 - Prob. 34PCh. 10.9 - Prob. 35PCh. 10.9 - Prob. 36PCh. 10.9 - Prob. 37PCh. 10.9 - Prob. 38PCh. 10.9 - Prob. 39PCh. 10.10 - Prob. 1APCh. 10.10 - Prob. 2APCh. 10.10 - Prob. 3APCh. 10.10 - Prob. 4APCh. 10.10 - Prob. 5APCh. 10.10 - Prob. 7APCh. 10.10 - Prob. 8APCh. 10.10 - Prob. 9APCh. 10.10 - Prob. 10APCh. 10.10 - For Problems 11-19, use properties of the Laplace...Ch. 10.10 - Prob. 12APCh. 10.10 - Prob. 13APCh. 10.10 - Prob. 14APCh. 10.10 - For Problems 11-19, use properties of the Laplace...Ch. 10.10 - Prob. 16APCh. 10.10 - Prob. 17APCh. 10.10 - Prob. 18APCh. 10.10 - Prob. 19APCh. 10.10 - Prob. 20APCh. 10.10 - For Problems 20-25, determine a function f(t) that...Ch. 10.10 - For problems 20-25, determine a function f(t) that...Ch. 10.10 - For problems 20-25, determine a function f(t) that...Ch. 10.10 - For problems 20-25, determine a function f(t) that...Ch. 10.10 - For problems 20-25, determine a function f(t) that...Ch. 10.10 - Prob. 26APCh. 10.10 - For Problems 26-28, sketch f(t), express f(t) in...Ch. 10.10 - For Problems 26-28, sketch f(t), express f(t) in...Ch. 10.10 - Prob. 29APCh. 10.10 - Prob. 30APCh. 10.10 - Prob. 31APCh. 10.10 - Let y(t) be the solution to the initial-value...Ch. 10.10 - Show that the general solution to the...Ch. 10.10 - For Problems 34-40, use the Laplace transform to...Ch. 10.10 - For Problems 34-40, use the Laplace transform to...Ch. 10.10 - For Problems 34-40, use the Laplace transform to...Ch. 10.10 - For Problems 34-40, use the Laplace transform to...Ch. 10.10 - For Problems 34-40, use the Laplace transform to...Ch. 10.10 - Prob. 39APCh. 10.10 - For Problems 34-40, use the Laplace transform to...Ch. 10.10 - For Problems 41-44, use the Laplace transform to...Ch. 10.10 - For Problems 41-44, use the Laplace transform to...Ch. 10.10 - For Problems 41-44, use the Laplace transform to...Ch. 10.10 - For Problems 41-44, use the Laplace transform to...Ch. 10.10 - Prob. 45APCh. 10.10 - Prob. 46APCh. 10.10 - For Problems 45-48, use the Laplace transform to...Ch. 10.10 - Prob. 48AP
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