## Solutions for Differential Equations: An Introduction to Modern Methods and Applications

Problem 1P:

Newton’s Law of Cooling. A cup of hot coffee has a temperature of when freshly poured, and is left...Problem 2P:

Blood plasma is stored at . Before it can be used, it must be at . When the plasma is placed an...Problem 3P:

At 11:09p.m. a forensics expert arrives at a crime scene where a dead body has just been found....Problem 4P:

The rate constant if the population doubles in days. Where a population of field mice that grows...Problem 5P:

The field mouse population in Example 3 satisfies the differential equation dp/dt=0.5p450. Find the...Problem 6P:

Radioactive Decay. Experiments show that a radioisotope decays at a rate negatively proportional to...Problem 7P:

A radioactive material, such as the isotope thorium 234, disintegrates at a rate proportional to the...Problem 8P:

Classical Mechanics. The differential equation for the velocity v of an objects of mass m,...Problem 9P:

For small, slowly falling objects, the assumption made inEq. (i) of Problem 8 that the drag force is...Problem 10P:

Mixing Problems. Many physical systems can be cast in the form of a mixing tank problem. Consider a...Problem 11P:

Mixing Problems. Many physical systems can be cast in the form of a mixing tank problem. Consider a...Problem 12P:

Mixing Problems. Many physical systems can be cast in the form of a mixing tank problem. Consider a...Problem 13P:

Pharmacokinetics. A simple model for the concentration of a drug administered to a patient is based...Problem 14P:

A certain drug is being administered intravenously to a hospital patient. Fluid containing of the...Problem 15P:

Continuously Compounded Interest. The amount of money in an interest bearing account in which the...Problem 16P:

Continuously Compounded Interest. The amount of money P(t) in an interest bearing account in which...Problem 17P:

Continuously Compounded Interest. The amount of money in an interest bearing account in which the...Problem 18P:

Continuously Compounded Interest. The amount of money in an interest bearing account in which the...# Browse All Chapters of This Textbook

Chapter 1.1 - Mathematical Models And SolutionsChapter 1.2 - Qualitative Methods: Phase Lines And Direction FieldsChapter 1.3 - Definitions, Classification, And TerminologyChapter 2.1 - Separable EquationsChapter 2.2 - Linear Equations: Method Of Integrating FactorsChapter 2.3 - Modeling With First Order EquationsChapter 2.4 - Differences Between Linear And Nonlinear EquationsChapter 2.5 - Autonomous Equations And Population DynamicsChapter 2.6 - Exact Equations And Integrating FactorsChapter 2.7 - Substitution Methods

Chapter 2.P1 - Harvesting A Renewable ResourceChapter 2.P2 - A Mathematical Model Of A Groundwater Contaminant SourceChapter 2.P3 - Monte Carlo Option Pricing: Pricing Financial Options By Flipping A CoinChapter 3.1 - Systems Of Two Linear Algebraic EquationsChapter 3.2 - Systems Of Two First Order Linear Differential EquationsChapter 3.3 - Homogeneous Linear Systems With Constant CoefficientsChapter 3.4 - Complex EigenvaluesChapter 3.5 - Repeated EigenvaluesChapter 3.6 - A Brief Introduction To Nonlinear SystemsChapter 3.P1 - Estimating Rate Constants For An Open Two-compartment ModelChapter 3.P2 - A Blood–brain Pharmacokinetic ModelChapter 4.1 - Definitions And ExamplesChapter 4.2 - Theory Of Second Order Linear Homogeneous EquationsChapter 4.3 - Linear Homogeneous Equations With Constant CoefficientsChapter 4.4 - Mechanical And Electrical VibrationsChapter 4.5 - Nonhomogeneous Equations; Method Of Undetermined CoefficientsChapter 4.6 - Forced Vibrations, Frequency Response, And ResonanceChapter 4.7 - Variation Of ParametersChapter 4.P1 - A Vibration Insulation ProblemChapter 4.P2 - Linearization Of A Nonlinear Mechanical SystemChapter 4.P3 - A Spring-mass Event ProblemChapter 4.P4 - Euler–lagrange EquationsChapter 5.1 - Definition Of The Laplace TransformChapter 5.2 - Properties Of The Laplace TransformChapter 5.3 - The Inverse Laplace TransformChapter 5.4 - Solving Differential Equations With Laplace TransformsChapter 5.5 - Discontinuous Functions And Periodic FunctionsChapter 5.6 - Differential Equations With Discontinuous Forcing FunctionsChapter 5.7 - Impulse FunctionsChapter 5.8 - Convolution Integrals And Their ApplicationsChapter 5.9 - Linear Systems And Feedback ControlChapter 5.P1 - An Electric Circuit ProblemChapter 5.P2 - The Watt Governor, Feedback Control, And StabilityChapter 6.1 - Definitions And ExamplesChapter 6.2 - Basic Theory Of First Order Linear SystemsChapter 6.3 - Homogeneous Linear Systems With Constant CoefficientsChapter 6.4 - Nondefective Matrices With Complex EigenvaluesChapter 6.5 - Fundamental Matrices And The Exponential Of A MatrixChapter 6.6 - Nonhomogeneous Linear SystemsChapter 6.7 - Defective MatricesChapter 6.P1 - Earthquakes And Tall BuildingsChapter 6.P2 - Controlling A Spring-mass System To EquilibriumChapter 7.1 - Autonomous Systems And StabilityChapter 7.2 - Almost Linear SystemsChapter 7.3 - Competing SpeciesChapter 7.4 - Predator–prey EquationsChapter 7.5 - Periodic Solutions And Limit CyclesChapter 7.6 - Chaos And Strange Attractors: The Lorenz EquationsChapter 7.P1 - Modeling Of EpidemicsChapter 7.P2 - Harvesting In A Competitive EnvironmentChapter 7.P3 - The R ̈ossler SystemChapter 8.1 - Numerical Approximations: Euler’s MethodChapter 8.2 - Accuracy Of Numerical MethodsChapter 8.3 - Improved Euler And Runge–kutta MethodsChapter 8.4 - Numerical Methods For Systems Of First Order EquationsChapter 8.P1 - Designing A Drip Dispenser For A Hydrology ExperimentChapter 8.P2 - Monte Carlo Option Pricing: Pricing Financial Options By Flipping A CoinChapter A.1 - MatricesChapter A.2 - Systems Of Linear Algebraic Equations, Linear Independence, And RankChapter A.3 - Determinants And InversesChapter A.4 - The Eigenvalue Problem

### Book Details

The modern landscape of technology and industry demands an equally modern approach to differential equations in the classroom. Designed for a first course in differential equations, the third edition of Brannan/Boyce’s Differential Equations: An Introduction to Modern Methods and Applications is consistent with the way engineers and scientists use mathematics in their daily work. The text emphasizes a systems approach to the subject and integrates the use of modern computing technology in the context of contemporary applications from engineering and science. The focus on fundamental skills, careful application of technology, and practice in modeling complex systems prepares students for the realities of the new millennium, providing the building blocks to be successful problem-solvers in today’s workplace. Section exercises throughout the text provide hands-on experience in modeling, analysis, and computer experimentation. Projects at the end of each chapter provide additional opportunities for students to explore the role played by differential equations in the sciences and engineering.

# Sample Solutions for this Textbook

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# More Editions of This Book

Corresponding editions of this textbook are also available below:

Differential Equations: An Introduction to Modern Methods and Applications - 2nd Edition

2nd Edition

ISBN: 9780470458242

Differential Equations With Boundary Value Problems: Modern Methods And Applications

2nd Edition

ISBN: 9780470902141

Differential Equations With Boundary Value Problems: An Introduction To Modern Methods And Applications

1st Edition

ISBN: 9780470418505

Differential Equations: An Introduction To Modern Methods And Applications

1st Edition

ISBN: 9780471651413

Differential Equations, Student Solutions Manual: An Introduction To Modern Methods And Applications

1st Edition

ISBN: 9780470125533

Differential Equations: An Introduction To Modern Methods And Applications Wileyplus Set

7th Edition

ISBN: 9780470132036

Differential Equations: An Introduction To Modern Methods And Applications 1st Edition With Wiley Plus Webct Powerpack Set

1st Edition

ISBN: 9780470136188

DIFFERENTIAL EQUATIONS-WILEYPLUS

3rd Edition

ISBN: 9781118981276

DIFFERENTIAL EQUATIONS (LL)-W/2 ACCESS

3rd Edition

ISBN: 9781119426271

Differential Equations, Binder Ready Version: An Introduction To Modern Methods And Applications

3rd Edition

ISBN: 9781118981221

DIFF EQUA--EBOOK+WILEY PLUS (CODE ONLY

3rd Edition

ISBN: 9781118981313

DIFFERENTIAL EQUATIONS W/WILEYPLUS

3rd Edition

ISBN: 9781119764618

DIFFERENTIAL EQUATIONS(LL) W/WILEYPLUS

3rd Edition

ISBN: 9781119764601

DIFFERENTIAL EQUATIONS-NEXTGEN WILEYPLUS

3rd Edition

ISBN: 9781119764564

EBK DIFFERENTIAL EQUATIONS

3rd Edition

ISBN: 9781119042686

Differential Equations: An Introduction To Modern Methods And Applications 3e Binder Ready Version + Wileyplus Registration Card

3rd Edition

ISBN: 9781119031871

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