## Solutions for Differential Equations with Boundary-Value Problems (MindTap Course List)

Problem 1E:

In Problems 18 state the order of the given ordinary differential equation. Determine whether the...Problem 2E:

In Problems 18 state the order of the given ordinary differential equation. Determine whether the...Problem 3E:

In Problems 18 state the order of the given ordinary differential equation. Determine whether the...Problem 4E:

In Problems 18 state the order of the given ordinary differential equation. Determine whether the...Problem 5E:

In Problems 18 state the order of the given ordinary differential equation. Determine whether the...Problem 6E:

In Problems 18 state the order of the given ordinary differential equation. Determine whether the...Problem 7E:

In Problems 18 state the order of the given ordinary differential equation. Determine whether the...Problem 8E:

In Problems 18 state the order of the given ordinary differential equation. Determine whether the...Problem 9E:

In Problems 9 and 10 determine whether the given first-order differential equation is linear in the...Problem 10E:

In Problems 9 and 10 determine whether the given first-order differential equation is linear in the...Problem 11E:

In Problems 1114 verify that the indicated function is an explicit solution of the given...Problem 12E:

In Problems 1114 verify that the indicated function is an explicit solution of the given...Problem 13E:

In Problems 1114 verify that the indicated function is an explicit solution of the given...Problem 14E:

In Problems 1114 verify that the indicated function is an explicit solution of the given...Problem 15E:

In Problems 1518 verify that the indicated function y = (x) is an explicit solution of the given...Problem 16E:

In Problems 1518 verify that the indicated function y = (x) is an explicit solution of the given...Problem 17E:

In Problems 1518 verify that the indicated function y = (x) is an explicit solution of the given...Problem 18E:

In Problems 1518 verify that the indicated function y = (x) is an explicit solution of the given...Problem 19E:

In Problems 19 and 20 verify that the indicated expression is an implicit solution of the given...Problem 20E:

In Problems 19 and 20 verify that the indicated expression is an implicit solution of the given...Problem 21E:

In Problems 2124 verify that the indicated family of functions is a solution of the given...Problem 22E:

In Problems 2124 verify that the indicated family of functions is a solution of the given...Problem 23E:

In Problems 2124 verify that the indicated family of functions is a solution of the given...Problem 24E:

In Problems 2124 verify that the indicated family of functions is a solution of the given...Problem 25E:

In Problems 2528 use (12) to verify that the indicated function is a solution of the given...Problem 26E:

In Problems 2528 use (12) to verify that the indicated function is a solution of the given...Problem 27E:

In Problems 2528 use (12) to verify that the indicated function is a solution of the given...Problem 29E:

Verify that the piecewise-defined function y={x2,x0x2,x0 is a solution of the differential equation...Problem 30E:

In Example 7 we saw that y=1(x)=25x2 and y=2(x)=25x2 are solutions of dy/dx = x/y on the interval...Problem 31E:

In Problems 31-34 find values of m so that the function y = emx is a solution of the given...Problem 32E:

In Problems 31-34 find values of m so that the function y = emx is a solution of the given...Problem 33E:

In Problems 31-34 find values of m so that the function y = emx is a solution of the given...Problem 34E:

In Problems 31-34 find values of m so that the function y = emx is a solution of the given...Problem 35E:

In Problems 35 and 36 find values of m so that the function y = xm is a solution of the given...Problem 36E:

In Problems 35 and 36 find values of m so that the function y = xm is a solution of the given...Problem 37E:

In Problems 3740 use the concept that y = c, x , is a constant function if and only if y = 0 to...Problem 38E:

In Problems 3740 use the concept that y = c, x , is a constant function if and only if y = 0 to...Problem 39E:

In Problems 3740 use the concept that y = c, x , is a constant function if and only if y = 0 to...Problem 40E:

In Problems 3740 use the concept that y = c, x , is a constant function if and only if y = 0 to...Problem 42E:

In Problems 41 and 42 verify that the indicated pair of functions is a solution of the given system...Problem 44E:

Make up a differential equation that you feel confident possesses only the trivial solution y = 0....Problem 45E:

What function do you know from calculus is such that its first derivative is itself? Its first...Problem 46E:

What function (or functions) do you know from calculus is such that its second derivative is itself?...Problem 47E:

The function y = sin x is an explicit solution of the first-order differential equation dydx=1y2....Problem 48E:

Discuss why it makes intuitive sense to presume that the linear differential equation y + 2y + 4y =...Problem 51E:

The graphs of members of the one-parameter family x3 + y3 = 3cxy are called folia of Descartes....Problem 57E:

The normal form (5) of an nth-order differential equation is equivalent to (4) whenever both forms...Problem 58E:

Find a linear second-order differential equation F(x, y, y, y) = 0 for which y = c1x + c2x2 is a...Problem 59E:

Consider the differential equation dy/dx = ex2. (a) Explain why a solution of the DE must be an...# Browse All Chapters of This Textbook

Chapter 1 - Introduction To Differential EquationsChapter 1.1 - Definitions And TerminologyChapter 1.2 - Initial-value ProblemsChapter 1.3 - Differential Equations As Mathematical ModelsChapter 2 - First-order Differential EquationsChapter 2.1 - Solution Curves Without A SolutionChapter 2.2 - Separable EquationsChapter 2.3 - Linear EquationsChapter 2.4 - Exact EquationsChapter 2.5 - Solutions By Substitutions

Chapter 2.6 - A Numerical MethodChapter 3 - Modeling With First-order Differential EquationsChapter 3.1 - Linear ModelsChapter 3.2 - Nonlinear ModelsChapter 3.3 - Modeling With Systems Of First-order DesChapter 4 - Higher-order Differential EquationsChapter 4.1 - Preliminary Theory-linear EquationsChapter 4.2 - Reduction Of OrderChapter 4.3 - Homogeneous Linear Equations With Constant CoefficientsChapter 4.4 - Undetermined Coefficients-superposition ApproachChapter 4.5 - Undetermined Coefficients-annihilator ApproachChapter 4.6 - Variation Of ParametersChapter 4.7 - Cauchy-euler EquationsChapter 4.8 - Green's FunctionsChapter 4.9 - Solving Systems Of Linear Des By EliminationChapter 4.10 - Nonlinear Differential EquationsChapter 5 - Modeling With Higher-order Differential EquationsChapter 5.1 - Linear Models: Initial-value ProblemsChapter 5.2 - Linear Models: Boundary-value ProblemsChapter 5.3 - Nonlinear ModelsChapter 6 - Series Solutions Of Linear EquationsChapter 6.1 - Review Of Power SeriesChapter 6.2 - Solutions About Ordinary PointsChapter 6.3 - Solutions About Singular PointsChapter 6.4 - Special FunctionsChapter 7 - The Laplace TransformChapter 7.1 - Definition Of The Laplace TransformChapter 7.2 - Inverse Transforms And Transforms Of DerivativesChapter 7.3 - Operational Properties IChapter 7.4 - Operational Properties IiChapter 7.5 - The Dirac Delta FunctionChapter 7.6 - Systems Of Linear Differential EquationsChapter 8 - Systems Of Linear First-order Differential EquationsChapter 8.1 - Preliminary Theory-linear SystemsChapter 8.2 - Homogeneous Linear SystemsChapter 8.3 - Nonhomogeneous Linear SystemsChapter 8.4 - Matrix ExponentialChapter 9 - Numerical Solutions Of Ordinary Differential EquationsChapter 9.1 - Euler Methods And Error AnalysisChapter 9.2 - Runge-kutta MethodsChapter 9.3 - Multistep MethodsChapter 9.4 - Higher-order Equations And SystemsChapter 9.5 - Second-order Boundary-value ProblemsChapter 10 - Systems Of Nonlinear First-order Differential EquationsChapter 10.1 - Autonomous SystemsChapter 10.2 - Stability Of Linear SystemsChapter 10.3 - Linearization And Local StabilityChapter 10.4 - Autonomous Systems As Mathematical ModelsChapter 11 - Fourier SeriesChapter 11.1 - Orthogonal FunctionsChapter 11.2 - Fourier SeriesChapter 11.3 - Fourier Cosine And Sine SeriesChapter 11.4 - Sturm-liouville ProblemChapter 11.5 - Bessel And Legendre SeriesChapter 12 - Boundary-value Problems In Rectangular CoordinatesChapter 12.1 - Separable Partial Differential EquationsChapter 12.2 - Classical Pdes And Boundary-value ProblemsChapter 12.3 - Heat EquationChapter 12.4 - Wave EquationChapter 12.5 - Laplace's EquationChapter 12.6 - Nonhomogeneous Boundary-value ProblemsChapter 12.7 - Orthogonal Series ExpansionsChapter 12.8 - Higher-dimensional ProblemsChapter 13 - Boundary-value Problems In Other Coordinate SystemsChapter 13.1 - Polar CoordinatesChapter 13.2 - Polar And Cylindrical CoordinatesChapter 13.3 - Spherical CoordinatesChapter 14 - Integral TransformsChapter 14.1 - Error FunctionChapter 14.2 - Laplace TransformChapter 14.3 - Fourier IntegralChapter 14.4 - Fourier TransformsChapter 15 - Fourier TransformsChapter 15.1 - Laplace's EquationChapter A - Integral-defined FunctionsChapter B - Matrices

### Book Details

DIFFERENTIAL EQUATIONS WITH BOUNDARY-VALUE PROBLEMS, 9th Edition strikes a balance between the analytical, qualitative, and quantitative approaches to the study of Differential Equations. This proven text speaks to students of varied majors through a wealth of pedagogical aids, including an abundance of examples, explanations, "Remarks" boxes, and definitions. The book provides a thorough overview of the topics typically taught in a first course in Differential Equations as well as an introduction to boundary-value problems and partial Differential Equations written in a straightforward, readable, and helpful style.

# Sample Solutions for this Textbook

We offer sample solutions for Differential Equations with Boundary-Value Problems (MindTap Course List) homework problems. See examples below:

Chapter 1, Problem 1REChapter 2, Problem 1REChapter 3, Problem 1REChapter 4, Problem 1REChapter 5, Problem 1REChapter 6, Problem 1REChapter 7, Problem 1REChapter 8, Problem 1REGiven: The linear differential equation is y′=2lnxy such that y(1)=2 and the value of step size is...

The given statement is “The second-order differential equation x″+f(x′)+g(x)=0 can be written as a...Chapter 11, Problem 1REChapter 12, Problem 1REChapter 13, Problem 1REChapter 14, Problem 1REChapter 15, Problem 1REGiven: The quantity is Γ(6). Calculation: The quantity is Γ(6). It is known that, the value of gamma...Given that the matrix A is [45−69] and B is [−268−10]. It is known that two or more matrices can be...

# More Editions of This Book

Corresponding editions of this textbook are also available below:

Differential Equations With Boundary-value Problems

7th Edition

ISBN: 9780495108368

Differential Equations with Boundary-Value Problems

7th Edition

ISBN: 9781111798529

Differential Equations with Computer Lab Experiments

2nd Edition

ISBN: 9780534351731

EBK DIFFERENTIAL EQUATIONS WITH BOUNDAR

8th Edition

ISBN: 9780100452985

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8th Edition

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