## Solutions for Elementary Differential Equations

Problem 1P:

In each of Problems 1 through 6, draw a direction field for the given differential equation. Based...Problem 2P:

In each of Problems 1 through 6, draw a direction field for the given differential equation. Based...Problem 3P:

In each of Problems 1 through 6, draw a direction field for the given differential equation. Based...Problem 4P:

In each of Problems 1 through 6, draw a direction held for the given differential equation. Based on...Problem 5P:

In each of Problems 1 through 6, draw a direction held for the given differential equation. Based on...Problem 6P:

In each of Problems 1 through 6, draw a direction held for the given differential equation. Based on...Problem 7P:

In each of Problems 7 through 10, write down a differential equation of the form dy/dt = ay + b...Problem 11P:

In each of Problems 11 through 14, draw a direction field for the given differential equation. Based...Problem 15P:

Consider the following list of differential equations, some of which produced the direction fields...Problem 18P:

Consider the following list of differential equations, some of which produced the direction fields...Problem 19P:

Consider the following list of differential equations, some of which produced the direction fields...Problem 22P:

A spherical raindrop evaporates at a rate proportional to its surface area. Write a differential...Problem 23P:

Newton’s law of cooling states that the temperature of an object changes at a rate proportional to...Problem 24P:

A certain drug is being administered intravenously to a hospital patient. Fluid containing 5 mg/cm3...Problem 28P:

In each of Problems 26 through 33, draw a direction field for the given differential equation. Based...Problem 30P:

In each of Problems 26 through 33, draw a direction field for the given differential equation. Based...# Browse All Chapters of This Textbook

Chapter 1.1 - Some Basic Mathematical Models; Direction FieldsChapter 1.2 - Solutions Of Some Differential EquationsChapter 1.3 - Classification Of Differential EquationsChapter 2 - First Order Differential EquationsChapter 2.1 - Linear Equations; Method Of Integrating FactorsChapter 2.2 - Separable EquationsChapter 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 Factors

Chapter 2.7 - Numerical Approximations: Euler's MethodChapter 2.8 - The Existence And Uniqueness TheoremChapter 2.9 - First Order Differential EquationsChapter 3.1 - Homogeneous Equations With Constant CoefficientsChapter 3.2 - Solutions Of Linear Homogeneous Equations; The WronskianChapter 3.3 - Complex Roots Of The Characteristic EquationChapter 3.4 - Repeated Roots; Reduction Of OrderChapter 3.5 - Nonhomogeneous Equations; Method Of Undetermined CoefficientsChapter 3.6 - Variation Of ParametersChapter 3.7 - Mechanical And Electrical VibrationsChapter 3.8 - Forced VibrationsChapter 4.1 - General Theory Of Nth Order Linear EquationsChapter 4.2 - Homogeneous Equations With Constant CoefficientsChapter 4.3 - The Method Of Undetermined CoefficientsChapter 4.4 - The Method Of Variation Of ParametersChapter 5.1 - Review Of Power SeriesChapter 5.2 - Series Solutions Near An Ordinary Point, Part IChapter 5.3 - Series Solutions Near An Ordinary Point, Part IiChapter 5.4 - Euler Equations; Regular Singular PointsChapter 5.5 - Series Solutions Near A Regular Singular Point, Part IChapter 5.6 - Series Solutions Near A Regular Singular Point, Part IiChapter 5.7 - Bessel's EquationChapter 6.1 - Definition Of The Laplace TransformChapter 6.2 - Solution Of Initial Value ProblemChapter 6.3 - Step FunctionsChapter 6.4 - Differential Equations With Discontinuous Forcing FunctionsChapter 6.5 - Impulse FunctionsChapter 6.6 - The Convolution IntegralChapter 7.1 - IntroductionChapter 7.2 - Review Of MatricesChapter 7.3 - Systems Of Linear Algebraic Equations; Linear Independence, Eigenvalues, Eigen VectorsChapter 7.4 - Basic Theory Of Systems Of First Order Linear EquationsChapter 7.5 - Homogeneous Linear Systems With Constant CoefficientsChapter 7.6 - Complex EigenvaluesChapter 7.7 - Fundamental MatricesChapter 7.8 - Repeated EigenvaluesChapter 7.9 - Nonhomogeneous Linear SystemsChapter 8.1 - The Euler Of Tangent Line MethodChapter 8.2 - Improvements On The Euler MethodChapter 8.3 - The Runge-kutta MethodChapter 8.4 - Multistep MethodsChapter 8.5 - Systems Of First Order EquationsChapter 8.6 - More On Errors; StabilityChapter 9.1 - The Phase Plane: Linear SystemsChapter 9.2 - Autonomous Equations And StabilityChapter 9.3 - Locally Linear SystemsChapter 9.4 - Competing SpeciesChapter 9.5 - Predator-prey EquationsChapter 9.6 - Liapunov's Second MethodChapter 9.7 - Periodic Solutions And Limit CyclesChapter 9.8 - Chaos And Strange Attractors: The Lorenz Equations

### Book Details

Boyce/DiPrima is the best-seller in its market and extremely popular. The format remains unchanged, but exercises and examples have been updated to reflect the most current scenarios and topics.

# Sample Solutions for this Textbook

We offer sample solutions for Elementary Differential Equations homework problems. See examples below:

Definition used: The first order linear equation is of the form dydt+p(t)y=q(t) where p and q are...Formula used: The known trigonometric identity is that cosA−cosB=−2sin(A+B2)sin(A−B2). Calculation:...Formula used: The variation of parameters for higher order differential equations is...Theorem used: Let r1 and r2 be the roots of the indicial equation F(r)=r(r−1)+p0r+q0 with r1≥r2. If...Theorem used: If F(s)=L{f(t)} and G(s)=L{g(t)} both exist for s>a≥0, then H(s)=F(s)G(s)=L{h(t)},...The given system of equations is, x′=(2−13−2)x+(ett) It is noted that, the given system is a...Consider the initial value problem is y'=t+y−3, y(0)=2. Therefore, the given solution is...

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