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11th Edition

Ron Larson + 1 other

Publisher: Cengage Learning

ISBN: 9781337275378

Chapter 16, Problem 1RE

Textbook Problem

1 views

Testing for Exactness In Exercises 1 and 2, determinewhether the differential equation is exact.

To determine

Whether the differential equation

**Solution:**

The differential equation

**Given information:**

The given differential equation is

**Concept Used:**

Let *M* and *N* have continuous partial derivatives on an open disk *R*. The differential equation

is exact if and only if

**Calculation:**

First we will compare differential equation

We have

Since

Multivariable Calculus

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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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