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6th Edition

Ron Larson + 1 other

Publisher: Cengage Learning

ISBN: 9781285774770

Chapter 6.3, Problem 17E

Textbook Problem

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Finding a Particular Solution Using Separation of Variables III Exercises 17-26, find the particular solution of the differential equation that satisfies the initial condition.

**Differential Equation Initial Condition**

To determine

**To calculate:** The particular solution of differential equation

**Given:**

The differential equation is

**Formula used:**

The differential equation is in variable separable form, *y* and *x* respectively.

The integral formula is

**Calculation:**

Consider the differential equation,

Simplify,

This differential equation is of variable separable form,

Now, integrate both side,

Calculus: Early Transcendental Functions (MindTap Course List)

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Solving a Differential Equation In Exercises 1520,...Ch. 6 - Solving a Differential Equation In Exercises 1520,...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 InterestFine 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 - 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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...Ch. 6 - Solving a First-Order Linear Differential...Ch. 6 - Solving a First-Order Linear Differential...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 - Writing In Exercises 6769. write an example of the...Ch. 6 - Writing In Exercise 6769. write an example of the...Ch. 6 - Writing In Exercises 6769, write an example of the...Ch. 6 - Investment Let A(t) be the amount in a fund...Ch. 6 - Investment A retired couple plans to withdraw P...Ch. 6 - Investment Use the result of Exercise 70 to find...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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