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11th Edition

Ron Larson + 1 other

Publisher: Cengage Learning

ISBN: 9781337275378

Chapter 16.2, Problem 7E

Textbook Problem

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Verifying a SolutionIn Exercises 5-8, verify the solution of the differential equation. Then use a graphing utility to graph the particular solutions for several different values of

Solution Differential Equation

To determine

**To verify:**

The solution of the differential equation

**Given information:**

The given differential equation is

**Concept Used:**

If

**Calculation:**

The characteristics equation is

First, we have to find the solution of the characteristics equation

Here,

Substitute the value of

Therefore, the general solution of the given linear differential equation is

Multivariable Calculus

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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 - 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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