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11th Edition

Ron Larson + 1 other

Publisher: Cengage Learning

ISBN: 9781337275378

Chapter 16, Problem 57RE

Textbook Problem

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Think About It

(a) Explain how, by observation, you know that a form of a particular solution of the differential equation

(b) Use your explanation in part (a) to find a particular solution of the differential equation

(c) Compare the algebra requiredto find particular solutionsin parts (a) and (b) with that required when the form of theparticular solution is

**a)**

To determine

How, by observing you know that a form of a particular solution of the differential equation

**Given information:**

The given differential equation is

**b)**

To determine

**To calculate:** Using the explanation in part (a) find a particular solution of the differential equation

**c)**

To determine

Compare the algebra required to find the particular solutions in parts (a) and (b) with that required when the form of the particular solution is

Multivariable Calculus

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Do...Ch. 16.2 - Give a geometric argument to explain why the graph...Ch. 16.2 - Motion of a Spring In Exercise 55-58, match the...Ch. 16.2 - Motion of a Spring In Exercise 55-58, match the...Ch. 16.2 - Motion of a Spring In Exercise 55-58, match the...Ch. 16.2 - Motion of a Spring In Exercise 55-58, match the...Ch. 16.2 - Motion of a SpringIn Exercise 59-64, a 32-pound...Ch. 16.2 - Motion of a SpringIn Exercise 59-64, a 32-pound...Ch. 16.2 - Motion of a SpringIn Exercise 59-64, a 32-pound...Ch. 16.2 - Motion of a SpringIn Exercise 59-64, a 32-pound...Ch. 16.2 - Motion of a SpringIn Exercise 59-64, a 32-pound...Ch. 16.2 - Motion of a SpringIn Exercise 59-64, a 32-pound...Ch. 16.2 - Real Zeros The characteristics equation of the...Ch. 16.2 - Complex Zero The characteristics equation of the...Ch. 16.2 - True or False? In exercises 67-70, determine...Ch. 16.2 - True or False? In exercises 67-70, determine...Ch. 16.2 - True or False? In exercises 67-70, determine...Ch. 16.2 - True or False? In exercises 67-70, determine...Ch. 16.2 - Wronskian The Wronskian of two differentiable...Ch. 16.2 - Wronskian The Wronskian of two differentiable...Ch. 16.2 - Wronskian The Wronskian of two differentiable...Ch. 16.2 - Wronskian The Wronskian of two differentiable...Ch. 16.3 - Writing What is the form of the general solution...Ch. 16.3 - Choosing a MethodDetermine whether you woulduse...Ch. 16.3 - Method of Undetermined Coefficients InExercises...Ch. 16.3 - Method of Undetermined Coefficients In Exercises...Ch. 16.3 - Method of Undetermined Coefficients In Exercises...Ch. 16.3 - Method of Undetermined Coefficients In Exercises...Ch. 16.3 - Choosing the Form of the ParticularSolution In...Ch. 16.3 - Choosing the Form of the ParticularSolution In...Ch. 16.3 - Choosing the Form of the Particular Solution In...Ch. 16.3 - Choosing the Form of the Particular Solution In...Ch. 16.3 - Method of Undetermined CoefficientsIn Exercises...Ch. 16.3 - Method of Undetermined CoefficientsIn Exercises...Ch. 16.3 - Method of Undetermined CoefficientsIn Exercises...Ch. 16.3 - Method of Undetermined CoefficientsIn Exercises...Ch. 16.3 - Method of Undetermined CoefficientsIn Exercises...Ch. 16.3 - Method of Undetermined CoefficientsIn Exercises...Ch. 16.3 - Using Initial Conditions In Exercises 17-22, solve...Ch. 16.3 - Using Initial Conditions In Exercises 17-22, solve...Ch. 16.3 - Using Initial Conditions In Exercises 17-22, solve...Ch. 16.3 - Using Initial Conditions In Exercises 17-22, solve...Ch. 16.3 - Using Initial Conditions In Exercises 17-22, solve...Ch. 16.3 - Using Initial Conditions In Exercises 17-22, solve...Ch. 16.3 - Method of Variation of Parameters InExercises...Ch. 16.3 - Method of Variation of Parameters In Exercises...Ch. 16.3 - Method of Variation of Parameters In Exercises...Ch. 16.3 - Method of Variation of Parameters In Exercises...Ch. 16.3 - Method of Variation of Parameters In Exercises...Ch. 16.3 - Method of Variation of Parameters In Exercises...Ch. 16.3 - Electrical Circuits In Exercises 29 and 30, use...Ch. 16.3 - Electrical Circuits In Exercises 29 and 30, use...Ch. 16.3 - Motion of a Spring In Exercises 31-34, use the...Ch. 16.3 - Motion of a Spring In Exercises 31-34, use the...Ch. 16.3 - Motion of a Spring In Exercises 31-34, use the...Ch. 16.3 - Motion of a Spring In Exercises 31-34, use the...Ch. 16.3 - EXPLORING CONCEPTS Motion of a Spring Rewrite yh...Ch. 16.3 - HOW DO YOU SEE IT? The figure shows the particular...Ch. 16.3 - Motion of a SpringRefer to the differential...Ch. 16.3 - Solving a Differential Equation Solve the...Ch. 16.3 - True or False? In Exercises 39 and 40, determine...Ch. 16.3 - True or False? In Exercises 39 and 40, determine...Ch. 16.3 - PUTNAM EXAM CHALLENGE For all real x, the...Ch. 16.4 - CONCEPT CHECK Power Series Solution Method...Ch. 16.4 - CONCEPT CHECK Recursion Formula What is a...Ch. 16.4 - Power Series Solution In Exercises 3-6, use a...Ch. 16.4 - Power Series Solution In Exercises 3-6, use a...Ch. 16.4 - Power Series Solution In Exercises 3-6, use a...Ch. 16.4 - Power Series Solution In Exercises 3-6, use a...Ch. 16.4 - Finding Terms of a Power Series SolutionIn...Ch. 16.4 - Finding Terms of a Power Series SolutionIn...Ch. 16.4 - Approximation by Taylor Series In Exercises 9-14,...Ch. 16.4 - Approximation by Taylor Series In Exercises 9-14,...Ch. 16.4 - Approximation by Taylor Series In Exercises 9-14,...Ch. 16.4 - Approximation by Taylor Series In Exercises 9-14,...Ch. 16.4 - Approximation by Taylor Series In Exercises 9-14,...Ch. 16.4 - Approximation by Taylor Series In Exercises 9-14,...Ch. 16.4 - EXPLORING CONCEPTS Using Different MethodsIn...Ch. 16.4 - EXPLORING CONCEPTS Using Different MethodsIn...Ch. 16.4 - EXPLORING CONCEPTS Using Different MethodsIn...Ch. 16.4 - EXPLORING CONCEPTS Using Different MethodsIn...Ch. 16.4 - Investigation Consider the differential equation...Ch. 16.4 - HOW DO YOU SEE IT? 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 - Finding an Integrating Factor In Exercises 13-16,...Ch. 16 - Finding an Integrating Factor In Exercises 13-16,...Ch. 16 - Finding an Integrating Factor In Exercises 13-16,...Ch. 16 - Finding an Integrating Factor In Exercises 13-16,...Ch. 16 - Verifying a Solution In Exercises 17-18, verify...Ch. 16 - Verifying a Solution In Exercises 17 and 18,...Ch. 16 - Finding a General Solution In exercises 19-28,...Ch. 16 - Finding a General Solution In exercises 19-28,...Ch. 16 - Finding a General Solution In exercises 19-28,...Ch. 16 - Finding a General Solution In exercises 19-28,...Ch. 16 - Finding a General Solution In exercises 19-28,...Ch. 16 - Finding a General Solution In exercises 19-28,...Ch. 16 - Finding a General Solution In exercises 19-28,...Ch. 16 - Finding a General Solution In exercises 19-28,...Ch. 16 - Finding a General Solution In exercises 19-28,...Ch. 16 - Finding a General Solution In exercises 19-28,...Ch. 16 - 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: 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 - Finding a General Solution Find the general...Ch. 16 - Distinct Real Zeros Given that the characteristic...Ch. 16 - Limit of a Solution Given that a and b are...Ch. 16 - Trivial and Nontrivial Solutions Consider the...Ch. 16 - Eulers Differential Equation Eulers differential...Ch. 16 - Pendulum Consider a pendulum of length L that...Ch. 16 - Deflection of a Beam A horizontal beam with a...Ch. 16 - Damped Motion In Exercises 11-14, consider a...Ch. 16 - Damped Motion In Exercises 11-14, consider a...Ch. 16 - Damped Motion In Exercises 11-14, consider a...Ch. 16 - Damped Motion In Exercises 11-14, consider a...Ch. 16 - Airys Equation Consider Airys equation given in...Ch. 16 - ChebyshevsEquation ConsiderChebyshevs equation...Ch. 16 - Bessels Equation: Order Zero The differential...Ch. 16 - Bessels Equation: Order One The differential...Ch. 16 - Hermites Equation Consider Hermites Equation...Ch. 16 - Laguerres Equation Consider Laguerres Equation...

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