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Multivariable Calculus

11th Edition
Ron Larson + 1 other
Publisher: Cengage Learning
ISBN: 9781337275378
Chapter 16.2, Problem 54E
Textbook Problem
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Give a geometric argument to explain why the graph cannot be a solution of the differential equation. (It is not necessary to solve the differential equation).

a) y ' ' = y '

Chapter 16.2, Problem 54E, Give a geometric argument to explain why the graph cannot be a solution of the differential , example  1

b) y ' ' = 1 2 y '

Chapter 16.2, Problem 54E, Give a geometric argument to explain why the graph cannot be a solution of the differential , example  2

a)

To determine

To explain: The geometric argument that the graph cannot be a solution of the differential equation y''=y'.

Explanation of Solution

Given information:

The given graph is shown below:

The given differential equation is y''=y'.

Form the given graph, it is observed that the graph represents the equation of parabola y=x2.

Differentiate the function y=x2 with respect to x, we get

y'=2x

b)

To determine

To explain: The geometric argument that the graph cannot be a solution of the differential equation y''=12y'.

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Chapter 16 Solutions

Multivariable Calculus
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Ch. 16.1 - Solving an Exact Differential Equation In...Ch. 16.1 - Solving an Exact Differential EquationIn Exercises...Ch. 16.1 - Solving an Exact Differential Equation In...Ch. 16.1 - Solving an Exact Differential EquationIn Exercises...Ch. 16.1 - Graphical and Analytic Analysis In Exercises 15...Ch. 16.1 - Graphical and Analytic AnalysisIn Exercises 15 and...Ch. 16.1 - Finding a Particular Solution In Exercises17-22,...Ch. 16.1 - Finding a Particular SolutionIn Exercises 17-22,...Ch. 16.1 - Finding a Particular Solution In Exercises 17-22,...Ch. 16.1 - Finding a Particular SolutionIn Exercises 17-22,...Ch. 16.1 - Finding a Particular Solution In Exercises 17-22,...Ch. 16.1 - Finding a Particular SolutionIn Exercises 17-22,...Ch. 16.1 - Finding an Integrating Factor In Exercises 23-32,...Ch. 16.1 - Finding an Integrating Factor In Exercises 23-32,...Ch. 16.1 - Finding an Integrating Factor In Exercises 23-32,...Ch. 16.1 - Finding an Integrating Factor In Exercises 23-32,...Ch. 16.1 - Finding an Integrating Factor In Exercises 23-32,...Ch. 16.1 - Finding an Integrating Factor In Exercises 23-32,...Ch. 16.1 - Finding an Integrating Factor In Exercises 23-32,...Ch. 16.1 - Finding an Integrating Factor In Exercises 23-32,...Ch. 16.1 - Finding an Integrating Factor In Exercises 23-32,...Ch. 16.1 - Finding an Integrating Factor In Exercises 23-32,...Ch. 16.1 - Using an Integrating Factor In Exercises 33-36,...Ch. 16.1 - Using an Integrating Factor In Exercises 33-36,...Ch. 16.1 - Using an Integrating Factor In Exercises 33-36,...Ch. 16.1 - Using an Integrating Factor In Exercises 33-36,...Ch. 16.1 - Integrating Factor Show that each expression is...Ch. 16.1 - Integrating FactorShow that thedifferential...Ch. 16.1 - Tangent Curves In Exercises 39-42, use agraphing...Ch. 16.1 - Tangent Curves In Exercises 39-42, use a graphing...Ch. 16.1 - Tangent Curves In Exercises 39-42, use a graphing...Ch. 16.1 - Tangent Curves In Exercises 39-42, use a graphing...Ch. 16.1 - Finding an Equation of a Curve In Exercise 43 and...Ch. 16.1 - Finding an Equation of a Curve In Exercises 43 and...Ch. 16.1 - Cost In a manufacturing process where y=C(x)...Ch. 16.1 - HOW DO YOU SEE? 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Consider the differential...Ch. 16.4 - Verifying that a Series Converges In Exercises...Ch. 16.4 - Verifying that a Series Converges In Exercises...Ch. 16.4 - Verifying that a Series Converges In Exercises...Ch. 16.4 - Verifying that a Series Converges In Exercises...Ch. 16.4 - Airys Equation Find the first six terms of the...Ch. 16 - Testing for Exactness In Exercises 1 and 2,...Ch. 16 - Testing for Exactness In Exercises 1 and 2,...Ch. 16 - Solving an Exact Differential Equation In...Ch. 16 - Solving an Exact Differential Equation In...Ch. 16 - Solving an Exact Differential Equation In...Ch. 16 - Solving an Exact Differential Equation In...Ch. 16 - Graphical and Analytical Analysis In Exercise 7...Ch. 16 - Graphical and Analytical Analysis In Exercise 7...Ch. 16 - Finding a Particular Solution In Exercises 9-12,...Ch. 16 - Finding a Particular Solution In Exercises 9-12,...Ch. 16 - Finding a Particular Solution In Exercises 9-12,...Ch. 16 - Finding a Particular Solution In Exercises 9-12,...Ch. 16 - 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Finding a Particular Solution: Initial Conditions...Ch. 16 - Finding a Particular Solution: Initial Conditions...Ch. 16 - Finding a Particular Solution: Initial Conditions...Ch. 16 - Finding a Particular Solution: Boundary...Ch. 16 - Finding a Particular Solution: Boundary...Ch. 16 - Motion of a SpringIn Exercise 35-36, a 64-pound...Ch. 16 - Motion of a SpringIn Exercise 35-36, a 64-pound...Ch. 16 - Method of Undetermined Coefficients In...Ch. 16 - Method of Undetermined Coefficients In Exercises...Ch. 16 - Method of Undetermined Coefficients In Exercises...Ch. 16 - Method of Undetermined Coefficients In Exercises...Ch. 16 - Choosing the Form of the Particular Solution...Ch. 16 - Choosing the Form of the Particular Solution In...Ch. 16 - Method of Undetermined Coefficients In Exercises43...Ch. 16 - Method of Undetermined Coefficients In Exercises...Ch. 16 - Using Initial Conditions In Exercises 45-50, solve...Ch. 16 - Using Initial Conditions In Exercises 45-50, solve...Ch. 16 - Using Initial Conditions In Exercises 45-50, solve...Ch. 16 - Using Initial Conditions In Exercises 45-50, solve...Ch. 16 - Using Initial Conditions In Exercises 45-50, solve...Ch. 16 - Using Initial Conditions In Exercises 45-50, solve...Ch. 16 - Method of Variation of Parameters In Exercises...Ch. 16 - Method of Variation of Parameters In Exercises...Ch. 16 - Method of Variation of Parameters In Exercises...Ch. 16 - Method of Variation of Parameters In Exercises...Ch. 16 - Electrical Circuit The differential equation...Ch. 16 - Investigation The differential equation...Ch. 16 - Think About It (a) Explain how, by observation,...Ch. 16 - Think About It Explain how you can find a...Ch. 16 - Power Series Solution In Exercises 59 and 60, use...Ch. 16 - Power Series Solution In Exercises 59 and 60, use...Ch. 16 - Approximation by Taylor Series In Exercises 61 and...Ch. 16 - Approximation by Taylor Series In Exercises 61 and...Ch. 16 - Finding a General Solution Find the value of k...Ch. 16 - Using an Integrating Factor The differential...Ch. 16 - Finding a General Solution Find the general...Ch. 16 - 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