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Slope Field In Exercises 11 and 12, (a) sketch the slope field for the differential equation, and (b) use the slope field to sketch the solution that passes through the given point. Use a graphing utility to verify your results. To print a blank coordinate plane, go to MathGraphs.com. y ' = y + 4 x , ( − 1 , 1 )

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Calculus: Early Transcendental Fun...

6th Edition
Ron Larson + 1 other
Publisher: Cengage Learning
ISBN: 9781285774770

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Chapter
Section
BuyFindarrow_forward

Calculus: Early Transcendental Fun...

6th Edition
Ron Larson + 1 other
Publisher: Cengage Learning
ISBN: 9781285774770
Chapter 6, Problem 12RE
Textbook Problem
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Slope Field In Exercises 11 and 12, (a) sketch the slope field for the differential equation, and (b) use the slope field to sketch the solution that passes through the given point. Use a graphing utility to verify your results. To print a blank coordinate plane, go to MathGraphs.com.

y ' = y + 4 x , ( 1 , 1 )

(a)

To determine

To graph: The slope field for the differential equation y=y+4x.

Explanation of Solution

Given: The provided differential equation y=y+4x with initial condition (1,1).

Graph:

Consider the differential equation y=y+4x.

Make a table representing the slopes at several points. The slopes at different points should be calculate to get a slope field.

Take several points to create a table for slope field.

x32211001122y111111111

(b)

To determine

To graph: The solution of the differential equation y=y+4x that passes through the point

(1,1).

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Chapter 6 Solutions

Calculus: Early Transcendental Functions (MindTap Course List)
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In Exercises 65 and 66, determine...Ch. 6.5 - True or False? In Exercises 65 and 66, determine...Ch. 6.6 - Analyzing Predator-Prey Equations In Exercises 3...Ch. 6.6 - Analyzing Predator-Prey EquationsIn Exercises 14,...Ch. 6.6 - Analyzing Predator-Prey EquationsIn Exercises 14,...Ch. 6.6 - Analyzing Predator-Prey Equations In Exercises 3...Ch. 6.6 - Predator-Prey Equations and Slope Fields In...Ch. 6.6 - Predator-Prey Equations and Slope Fields In...Ch. 6.6 - Predator-Prey Equations and Slope Fields In...Ch. 6.6 - Predator-Prey Equations and Slope Fields In...Ch. 6.6 - Rabbits and Foxes In Exercises 9-12, consider a...Ch. 6.6 - Rabbits and Foxes In Exercises 9-12, consider a...Ch. 6.6 - Rabbits and Foxes In Exercises 9-12, consider a...Ch. 6.6 - Rabbits and Foxes In Exercises 9-12, consider a...Ch. 6.6 - Prairie Dogs and Black-Footed Ferrets In Exercises...Ch. 6.6 - Prairie Dogs and Black-Footed Ferrets In Exercises...Ch. 6.6 - Prairie Dogs and Black-Footed Ferrets In Exercises...Ch. 6.6 - Prairie Dogs and Black-Footed Ferrets In Exercises...Ch. 6.6 - Critical Point as the Initial Condition In...Ch. 6.6 - Critical Point as the Initial Condition In...Ch. 6.6 - Analyzing Competing-Species Equations In Exercises...Ch. 6.6 - Analyzing Competing-Species Equations In Exercises...Ch. 6.6 - Analyzing Competing-Species Equations In Exercises...Ch. 6.6 - Analyzing Competing-Species Equations In Exercises...Ch. 6.6 - Bass and Trout In Exercises 23 and 24, consider a...Ch. 6.6 - Bass and Trout In Exercises 23 and 24, consider a...Ch. 6.6 - Bass and Trout In Exercises 25 and 26, consider a...Ch. 6.6 - Bass and Trout In Exercises 25 and 26, consider a...Ch. 6.6 - Critical Point as the Initial Condition In...Ch. 6.6 - Critical Point as the Initial Condition In...Ch. 6.6 - WRITING ABOUT CONCEPTS Separation of Variables Are...Ch. 6.6 - EXPLORING CONCEPTS Determining Initial Values...Ch. 6.6 - Determining Initial Values Given a set of compete...Ch. 6.6 - HOW DO YOU SEE IT? The populations of two species...Ch. 6.6 - Revising the Predator-Prey Equations Consider a...Ch. 6 - Determining a Solution Determine whether the...Ch. 6 - Determining a Solution Determine whether the...Ch. 6 - Finding a General Solution In Exercises 3-8, use...Ch. 6 - Finding a General SolutionIn Exercises 38, use...Ch. 6 - Finding a General Solution In Exercises 3-8, use...Ch. 6 - Finding a General Solution In Exercises 38, use...Ch. 6 - Finding a General Solution In Exercises 3-8, use...Ch. 6 - Finding a General Solution In Exercises 3-8, use...Ch. 6 - Slope Field In Exercises 9 and 10, a differential...Ch. 6 - Slope Field In Exercises 9 and 10, a differential...Ch. 6 - Slope Field In Exercises 11 and 12, (a) sketch the...Ch. 6 - Slope Field In Exercises 11 and 12, (a) sketch the...Ch. 6 - Euler's Method In Exercises 13 and 14, use Eulers...Ch. 6 - Euler's Method In Exercises 13 and 14, use Eulers...Ch. 6 - Solving a Differential Equation In Exercises 1520,...Ch. 6 - Solving a Differential Equation In Exercises 1520,...Ch. 6 - Solving a Differential Equation In Exercises 1520,...Ch. 6 - Solving a Differential Equation In Exercises 1520,...Ch. 6 - Solving a Differential Equation In Exercises...Ch. 6 - Solving a Differential Equation In Exercises...Ch. 6 - Writing and Solving a Differential Equation In...Ch. 6 - Writing and Solving a Differential Equation In...Ch. 6 - Finding an Exponential Function In Exercises...Ch. 6 - Finding an Exponential Function In Exercises...Ch. 6 - Finding an Exponential Function In Exercises...Ch. 6 - Finding an Exponential Function In Exercises...Ch. 6 - Air Pressure Under ideal conditions, air pressure...Ch. 6 - Radioactive Decay Radioactive radium has a...Ch. 6 - Population A population grows exponentially at a...Ch. 6 - Compound InterestFine the balance in an account...Ch. 6 - Sales The sales S (in thousands of units) of a new...Ch. 6 - Sales The sales 5 (in thousands of units) of a new...Ch. 6 - Finding a General Solution Using Separation of...Ch. 6 - Finding a General Solution Using Separation of...Ch. 6 - Finding a General Solution Using Separation of...Ch. 6 - Finding a General Solution Using Separation of...Ch. 6 - Finding a Particular Solution Using Separation of...Ch. 6 - Finding a Particular Solution Using Separation of...Ch. 6 - Finding a Particular Solution Using Separation of...Ch. 6 - Finding a Particular Solution Using Separation of...Ch. 6 - Slope Field In Exercises 43 and 44, sketch a few...Ch. 6 - Slope Field In Exercises 43 and 44, sketch a few...Ch. 6 - Using a Logistic Equation In Exercises 49 and 50,...Ch. 6 - Using a Logistic Equation In Exercises 49 and 50,...Ch. 6 - Solving a Logistic Differential Equation In...Ch. 6 - Solving a Logistic Differential Equation In...Ch. 6 - Environment A conservation department releases...Ch. 6 - Environment Write a logistic differential equation...Ch. 6 - Sales Growth The rate of change in sales 5 (in...Ch. 6 - Sales Growth Use the result of Exercise 55 to...Ch. 6 - Learning Theory In Exercises 57 and 58, assume...Ch. 6 - Learning Theory In Exercises 57 and 58, assume...Ch. 6 - Solving a First-Order Linear Differential Equation...Ch. 6 - Solving a First-Order Linear Differential Equation...Ch. 6 - Solving a First-Order Linear Differential Equation...Ch. 6 - Solving a First-Order Linear Differential...Ch. 6 - Solving a First-Order Linear Differential...Ch. 6 - Solving a First-Order Linear Differential...Ch. 6 - Solving a First-Order Linear Differential Equation...Ch. 6 - Solving a First-Order Linear Differential Equation...Ch. 6 - Slope Field In Exercises 67-70, (a) sketch an...Ch. 6 - Slope Field In Exercises 67-70, (a) sketch an...Ch. 6 - Slope Field In Exercises 67-70, (a) sketch an...Ch. 6 - Slope Field In Exercises 67-70, (a) sketch an...Ch. 6 - Finding a Particular Solution In Exercises 71-74,...Ch. 6 - Finding a Particular Solution In Exercises 71-74,...Ch. 6 - Writing In Exercises 6769. write an example of the...Ch. 6 - Writing In Exercise 6769. write an example of the...Ch. 6 - Writing In Exercises 6769, write an example of the...Ch. 6 - Investment Let A(t) be the amount in a fund...Ch. 6 - Investment A retired couple plans to withdraw P...Ch. 6 - Investment Use the result of Exercise 70 to find...Ch. 6 - Analyzing Predator-Prey Equations In Exercises 79...Ch. 6 - Analyzing Predator-Prey Equations In Exercises 79...Ch. 6 - Analyzing Competing-Species Equations In Exercises...Ch. 6 - Analyzing Competing-Species Equations In Exercises...Ch. 6 - Doomsday Equation The differential equation where...Ch. 6 - Sales Let S represent sales of a new product (in...Ch. 6 - Error Using the Product Rule Although it is true...Ch. 6 - Torricellis Law Torricellis Law states that water...Ch. 6 - Torricelli's Law The cylindrical water tank shown...Ch. 6 - Torricelli's Law A tank similar to the one in...Ch. 6 - Rewriting the Logistic Equation Show that the...Ch. 6 - Biomass Biomass is a measure of the amount of...Ch. 6 - Finding a Function Consider a function f such that...Ch. 6 - If the tracer is injected instantaneously at time...Ch. 6 - Use the solution of the differential equation in...Ch. 6 - In Exercises 11 and 12, it was assumed that there...

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