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Differential Equations with Boundary-Va...

9th Edition

Dennis G. Zill

Publisher: Cengage Learning

ISBN: 9781305965799

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Chapter

Section

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 28E:

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 41E:

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

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 49E:

In Problems 49 and 50 the given figure represents the graph of an implicit solution G(x, y) = 0 of a...

Problem 50E:

In Problems 49 and 50 the given figure represents the graph of an implicit solution G(x, y) = 0 of a...

Problem 51E:

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

Problem 52E:

The graph in Figure 1.1.7 is the member of the family of folia in Problem 51 corresponding to c = 1....

Problem 53E:

In Example 7 the largest interval I over which the explicit solutions y = 1(x) and y = 2(x) are...

Problem 54E:

In Problem 21 a one-parameter family of solutions of the DE P = P(1 P) is given. Does any solution...

Problem 55E:

Discuss, and illustrate with examples, how to solve differential equations of the forms dy/dx = f(x)...

Problem 56E:

The differential equation x(y)2 4y 12x3 = 0 has the form given in (4). Determine whether the...

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...

Problem 60E:

Consider the differential equation dy/dx = 5 y. (a) Either by inspection or by the method suggested...

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

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.

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

In Problems 1 and 2 fill in the blank and then write this result as a linear first-order...Answer Problems 112 without referring back to the text. Fill in the blanks or answer true or false....Answer Problems 1 and 2 without referring back to the text. Fill in the blank or answer true or...Answer Problems 110 without referring back to the text. Fill in the blank or answer true or false....If a mass weighing 10 pounds stretches a spring 2.5 feet, a mass weighing 32 pounds will stretch it...In Problems 1 and 2 answer true or false without referring back to the text. 1. The general solution...In Problems 1 and 2 use the definition of the Laplace transform to find f(t). 1. f(t)={t,0t12t,t1fill in the blanks. 1. The vector X=k(45) is a solution of X=(1421)X(81) for k = _____________.In Problems 1–4 construct a table comparing the indicated values of y(x) using Euler’s method, the...

Answer Problems 1-10 without referring back to the text. Fill in the blank, or answer true or false....In Problems 16 fill in the blank or answer true or false without referring back to the text. 1. The...Use separation of variables to find product solutions of 2uxy=u.Find the steady-state temperature u(r, θ) in a circular plate of radius c if the temperature on the...In Problems 1-20 solve the given boundary-value problem by an appropriate integral transform. Make...Consider the boundary-value problem 2ux2+2uy2=0,0x2,0y1u(0,y)=0,u(2,y)=50,0y1u(x,0)=0,u(x,1)=0,0x2...In Problems 1 and 2 evaluate the given quantity. 1. (6)If A=(4569) and B=(26810), find (a) A + B (b) B A (c) 2A + 3B

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