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11th Edition

Ron Larson + 1 other

Publisher: Cengage Learning

ISBN: 9781337275378

Chapter 16.1, Problem 10E

Textbook Problem

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Solving an Exact Differential Equation In Exercises 7–14, verify that the differential equation is exact. Then find the general solution.

To determine

Whether the differential equation

**Given information:**

The given differential equation is

**Concept Used:**

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

is exact if and only if

2) The equation *f* of two variables x and y having continuous partial derivatives such that

The general solution of the equation is

**Calculation:**

First we will compare differential equation

We have

Since

Multivariable Calculus

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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 - 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