Explanation Given information: The provided differential equation is 12.5 d v d t = 43.2 − 1.25 v . Formula Used: Integration formula: ∫ 1 a − b y d y = ln | a − b y | − b , ∫ k d x = k x + c Calculation: Consider the differential equation, 12.5 d v d t = 43.2 − 1.25 v The above differential equation can be written as, d v d t = 43.2 12.5 − 1.25 v 12.5 d v d t = 3.456 − 0.1 v Separate the variable by grouping the x variable on side and the y variable on other side, Therefore, d v d t = 3.456 − 0.1 v d v 3.456 − 0.1 v = d t Integrate each side of the above differential equation, Therefore, ∫ d v 3.456 − 0.1 v = ∫ d t Apply, integration formula ∫ 1 a − b y d y = ln | a − y | b , ∫ k d x = k x + c in ∫ d v 3.456 − 0.1 v = ∫ d t Therefore, ∫ d v 3.456 − 0.1 v = ∫ d t − 10 ln | 3.456 − 0.1 v | = t + c 1 ln | 3.456 − 0.1 v | = − t 10 − c 1 10 3.456 − 0.1 v = e − t 10 − c 1 10 Further simplify, 3.456 − 0.1 v = e − t 10 − c 1 10 3

Calculus: An Applied Approach (MindTap Course List)

10th Edition

ISBN: 9781305860919

Author: Ron Larson

Publisher: Cengage Learning

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Differential Equations

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Chapter 11.2, Problem 41E

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To calculate: The solution of the differential equation 12.5dvdt=43.2−1.25v at initial condition v=0,t=0.

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Chapter 11.2, Problem 40E

Chapter 11.2, Problem 42E

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Chapter 11 Solutions

Calculus: An Applied Approach (MindTap Course List)

Ch. 11.1 - Checkpoint 1 Worked-out solution available at...Ch. 11.1 - Prob. 2CP Ch. 11.1 - Prob. 3CP Ch. 11.1 - Prob. 4CP Ch. 11.1 - Prob. 1SWU Ch. 11.1 - Prob. 2SWU Ch. 11.1 - Prob. 3SWU Ch. 11.1 - Prob. 4SWU Ch. 11.1 - Prob. 5SWU Ch. 11.1 - Prob. 6SWU

Ch. 11.1 - Verifying Solutions In Exercises 112, verify the...Ch. 11.1 - Prob. 2E Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E Ch. 11.1 - Prob. 7E Ch. 11.1 - Prob. 8E Ch. 11.1 - Verifying Solutions In Exercises 1-12, verify the...Ch. 11.1 - Prob. 10E Ch. 11.1 - Prob. 11E Ch. 11.1 - Prob. 12E Ch. 11.1 - Prob. 13E Ch. 11.1 - Prob. 14E Ch. 11.1 - Determining Solutions In Exercises 1316, determine...Ch. 11.1 - Prob. 16E Ch. 11.1 - Determining Solutions In Exercises 1720, determine...Ch. 11.1 - Prob. 18E Ch. 11.1 - Prob. 19E Ch. 11.1 - Prob. 20E Ch. 11.1 - Prob. 21E Ch. 11.1 - Prob. 22E Ch. 11.1 - Prob. 23E Ch. 11.1 - Prob. 24E Ch. 11.1 - Prob. 25E Ch. 11.1 - Prob. 26E Ch. 11.1 - Prob. 27E Ch. 11.1 - Prob. 28E Ch. 11.1 - Prob. 29E Ch. 11.1 - Prob. 30E Ch. 11.1 - Prob. 31E Ch. 11.1 - Prob. 32E Ch. 11.1 - Prob. 33E Ch. 11.1 - Prob. 34E Ch. 11.1 - Prob. 35E Ch. 11.1 - Prob. 36E Ch. 11.1 - Prob. 37E Ch. 11.1 - Prob. 38E Ch. 11.1 - Prob. 39E Ch. 11.1 - Investment The rate of growth of an investment is...Ch. 11.1 - Prob. 41E Ch. 11.1 - Prob. 42E Ch. 11.1 - Prob. 43E Ch. 11.1 - Prob. 44E Ch. 11.1 - Prob. 45E Ch. 11.1 - Prob. 46E Ch. 11.2 - Checkpoint 1 Worked-out solution available at...Ch. 11.2 - Prob. 2CP Ch. 11.2 - Prob. 3CP Ch. 11.2 - Prob. 4CP Ch. 11.2 - Prob. 5CP Ch. 11.2 - Prob. 6CP Ch. 11.2 - Prob. 1SWU Ch. 11.2 - Prob. 2SWU Ch. 11.2 - Prob. 3SWU Ch. 11.2 - Prob. 4SWU Ch. 11.2 - Prob. 5SWU Ch. 11.2 - Prob. 6SWU Ch. 11.2 - Prob. 7SWU Ch. 11.2 - Prob. 8SWU Ch. 11.2 - Prob. 9SWU Ch. 11.2 - Prob. 10SWU Ch. 11.2 - Prob. 1E Ch. 11.2 - Prob. 2E Ch. 11.2 - Prob. 3E Ch. 11.2 - Prob. 4E Ch. 11.2 - Prob. 5E Ch. 11.2 - Prob. 6E Ch. 11.2 - Prob. 7E Ch. 11.2 - Prob. 8E Ch. 11.2 - Prob. 9E Ch. 11.2 - Prob. 10E Ch. 11.2 - Prob. 11E Ch. 11.2 - Prob. 12E Ch. 11.2 - Prob. 13E Ch. 11.2 - Solving a Differential Equation In Exercises 7-26,...Ch. 11.2 - Prob. 15E Ch. 11.2 - Prob. 16E Ch. 11.2 - Prob. 17E Ch. 11.2 - Prob. 18E Ch. 11.2 - Prob. 19E Ch. 11.2 - Prob. 20E Ch. 11.2 - Prob. 21E Ch. 11.2 - Prob. 22E Ch. 11.2 - Prob. 23E Ch. 11.2 - Prob. 24E Ch. 11.2 - Prob. 25E Ch. 11.2 - Prob. 26E Ch. 11.2 - Prob. 27E Ch. 11.2 - Prob. 28E Ch. 11.2 - Prob. 29E Ch. 11.2 - Prob. 30E Ch. 11.2 - Prob. 31E Ch. 11.2 - Finding a Particular Solution In Exercises 31-38,...Ch. 11.2 - Prob. 33E Ch. 11.2 - Finding a Particular Solution In Exercises 31-38,...Ch. 11.2 - Prob. 35E Ch. 11.2 - Finding a Particular Solution In Exercises 31-38,...Ch. 11.2 - Prob. 37E Ch. 11.2 - Prob. 38E Ch. 11.2 - Prob. 39E Ch. 11.2 - Prob. 40E Ch. 11.2 - Prob. 41E Ch. 11.2 - Prob. 42E Ch. 11.2 - Prob. 43E Ch. 11.2 - Prob. 44E Ch. 11.2 - Radioactive Decay The rate of decomposition of...Ch. 11.2 - Radioactive Decay The rate of decomposition of...Ch. 11.2 - Solve the differential equation. Weight Gain A...Ch. 11.2 - Prob. 1QY Ch. 11.2 - Prob. 2QY Ch. 11.2 - Prob. 3QY Ch. 11.2 - Prob. 4QY Ch. 11.2 - Prob. 5QY Ch. 11.2 - Prob. 6QY Ch. 11.2 - Prob. 7QY Ch. 11.2 - Prob. 8QY Ch. 11.2 - Prob. 9QY Ch. 11.2 - Prob. 10QY Ch. 11.2 - Prob. 11QY Ch. 11.2 - Prob. 12QY Ch. 11.2 - Prob. 13QY Ch. 11.2 - Prob. 14QY Ch. 11.2 - Prob. 15QY Ch. 11.2 - Ignoring resistance, a sailboat starting from rest...Ch. 11.3 - Checkpoint 1 Worked-out solution available at...Ch. 11.3 - Prob. 2CP Ch. 11.3 - Prob. 3CP Ch. 11.3 - Prob. 1SWU Ch. 11.3 - Prob. 2SWU Ch. 11.3 - Prob. 3SWU Ch. 11.3 - Prob. 4SWU Ch. 11.3 - Prob. 5SWU Ch. 11.3 - Prob. 6SWU Ch. 11.3 - Prob. 7SWU Ch. 11.3 - Prob. 8SWU Ch. 11.3 - In Exercises 5-10, find the indefinite integral....Ch. 11.3 - Prob. 10SWU Ch. 11.3 - Prob. 1E Ch. 11.3 - Prob. 2E Ch. 11.3 - Prob. 3E Ch. 11.3 - Prob. 4E Ch. 11.3 - Prob. 5E Ch. 11.3 - Prob. 6E Ch. 11.3 - Prob. 7E Ch. 11.3 - Prob. 8E Ch. 11.3 - Solving a Linear Differential Equation In...Ch. 11.3 - Prob. 10E Ch. 11.3 - 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The solution of the differential equation 12.5 d v d t = 43.2 − 1.25 v at initial condition v = 0 , t = 0 .

Solution Summary: The author calculates the solution of the differential equation 12.5dvt=43.2-1.25v at initial condition v=0,t =0.

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To calculate: The solution of the differential equation 12.5dvdt=43.2−1.25v at initial condition v=0,t=0.

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Chapter 11 Solutions