Math

CalculusCalculus: Early Transcendental FunctionsSolving a Bernoulli Differential Equation In Exercises 57-64, solve the Bernoulli differential equation. The Bernoulliequation is a well-known nonlinear equation of the form y ′ + P ( x ) y = Q ( x ) y ″ that can be reduced to a linear form by a substitution. The general solution of a Bernoulli equation is y 1 − n e ∫ ( 1 − n ) P ( x ) d x = ∫ ( 1 − n ) Q ( x ) e ∫ ( 1 − n ) P ( x ) d x d x + C . y ′ − y = e x y 3BuyFind*launch*

7th Edition

Ron Larson + 1 other

Publisher: Cengage Learning

ISBN: 9781337552516

Chapter 6.5, Problem 63E

Textbook Problem

Solving a Bernoulli Differential Equation In Exercises 57-64, solve the Bernoulli differential equation. The Bernoulliequation is a well-known nonlinear equation of the form

**that can be reduced to a linear form by a substitution. The general solution of a Bernoulli equation is**

Calculus: Early Transcendental Functions

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The graph shows the amount of...Ch. 6.5 - EXPLORING CONCEPTS Using Different Methods...Ch. 6.5 - Integrating Factor Explain why you can omit the...Ch. 6.5 - Matching In Exercises 43-46. match the...Ch. 6.5 - Matching In Exercises 43-46. match the...Ch. 6.5 - Matching In Exercises 43-46. match the...Ch. 6.5 - Matching In Exercises 43-46. match the...Ch. 6.5 - Slope Field In Exercises 47 and 48, (a) use a...Ch. 6.5 - Slope Field In Exercises 47 and 48, (a) use a...Ch. 6.5 - Solving a First-Order Differential Equation In...Ch. 6.5 - Solving a First-Order Differential Equation In...Ch. 6.5 - Solving a First-Order Differential Equation In...Ch. 6.5 - Solving a First-Order Differential Equation In...Ch. 6.5 - Solving a First-Order Differential Equation In...Ch. 6.5 - Solving a First-Order Differential Equation In...Ch. 6.5 - Solving a First-Order Differential Equation In...Ch. 6.5 - Solving a First-Order Differential Equation In...Ch. 6.5 - Solving a Bernoulli Differential Equation In...Ch. 6.5 - Solving a Bernoulli Differential Equation In...Ch. 6.5 - Solving a Bernoulli Differential Equation In...Ch. 6.5 - Solving a Bernoulli Differential Equation In...Ch. 6.5 - Solving a Bernoulli Differential Equation In...Ch. 6.5 - Solving a Bernoulli Differential Equation In...Ch. 6.5 - Solving a Bernoulli Differential Equation In...Ch. 6.5 - Solving a Bernoulli Differential Equation In...Ch. 6.5 - True or False? In Exercises 65 and 66, determine...Ch. 6.5 - True or False? In Exercises 65 and 66, determine...Ch. 6.6 - CONCEPT CHECK Autonomous Differential Equation...Ch. 6.6 - CONCEPT CHECK Competing Species Equations Which...Ch. 6.6 - Analyzing Predator-Prey Equations In Exercises 3...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 - EXPLORING CONCEPTS Determining Initial Values...Ch. 6.6 - HOW DO YOU SEE IT? 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Solving a Differential Equation In Exercises...Ch. 6 - Solving a Differential Equation In Exercises...Ch. 6 - Solving a Differential Equation In Exercises...Ch. 6 - Solving a Differential Equation In Exercises...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 Interest Find 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 - Finding a Particular Solution Curve In Exercises...Ch. 6 - Finding a Particular Solution Curve In Exercises...Ch. 6 - Finding Orthogonal Trajectories In Exercises 47...Ch. 6 - Finding Orthogonal Trajectories In Exercises 47...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 - Wildlife Population The rate of change of the...Ch. 6 - Environment A conservation department releases...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 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 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 - Finding a Particular Solution In Exercises 71-74,...Ch. 6 - Finding a Particular Solution In Exercises 71-74,...Ch. 6 - Investment Let A(t) be the amount in a fund...Ch. 6 - Investment A retired couple plans to withdraw P...Ch. 6 - Falling Object A 12-pound object is dropped from...Ch. 6 - Mixture A tank contains 100 gallons of a solution...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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