A First Course in Differential Equation...11th EditionZILL, Dennis G. Publisher: Cengage LearningISBN: 9781337293129
A First Course in Differential Equation...
Solutions for A First Course in Differential Equations with Modeling Applications, Loose-leaf Version
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 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 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 58E:
Find a linear second-order differential equation F(x, y, y, y) = 0 for which y = c1x + c2x2 is a...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 A - Integral-defined FunctionsChapter B - Matrices
Book Details
A FIRST COURSE IN DIFFERENTIAL EQUATIONS WITH MODELING APPLICATIONS, 11th Edition, strikes a balance between analytical, qualitative, and quantitative approaches to the study of differential equations. This proven resource speaks to students of varied majors through a wealth of pedagogical aids, including an abundance of examples, explanations, "Remarks" boxes, and definitions. Now fully supported by two strong digital learning solutions, Enhanced WebAssign and MindTap Math, it provides a thorough overview of the topics typically taught in a first course in differential equations written in a straightforward, readable, and helpful style.
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A First Course in Differential Equations: The Classic Fifth Edition
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