Solutions for First Course in Differential Equations (Instructor's)
Problem 1E:
In Problems 14 reproduce the given computer-generated direction field. Then sketch, by hand, an...Problem 2E:
In Problems 14 reproduce the given computer-generated direction field. Then sketch, by hand, an...Problem 3E:
dydx=1xy (a) y(0) = 0 (b) y(1) = 0 (c) y(2) = 2 (d) y(0) = 4 FIGURE 2.1.14 Direction field for...Problem 4E:
In Problems 14 reproduce the given computer-generated direction field. Then sketch, by hand, an...Problem 5E:
In Problems 512 use computer software to obtain a direction field for the given differential...Problem 6E:
In Problems 512 use computer software to obtain a direction field for the given differential...Problem 7E:
In Problems 512 use computer software to obtain a direction field for the given differential...Problem 8E:
In Problems 512 use computer software to obtain a direction field for the given differential...Problem 9E:
In Problems 512 use computer software to obtain a direction field for the given differential...Problem 10E:
In Problems 512 use computer software to obtain a direction field for the given differential...Problem 11E:
In Problems 512 use computer software to obtain a direction field for the given differential...Problem 12E:
In Problems 512 use computer software to obtain a direction field for the given differential...Problem 13E:
In Problems 13 and 14 the given figure represents the graph of f(y) and f(x), respectively. By hand,...Problem 14E:
In Problems 13 and 14 the given figure represents the graph of f(y) and f(x), respectively. By hand,...Problem 15E:
In parts (a) and (b) sketch isoclines f(x, y) = c (see the Remarks on page 39) for the given...Problem 16E:
(a) Consider the direction field of the differential equation dy/dx = x(y 4)2 2, but do not use...Problem 19E:
Consider the autonomous first-order differential equation dy/dx = y y3 and the initial condition...Problem 20E:
Consider the autonomous first-order differential equation dy/dx = y2 y4 and the initial condition...Problem 21E:
In Problems 21-28 find the critical points and phase portrait of the given autonomous first-order...Problem 22E:
In Problems 21-28 find the critical points and phase portrait of the given autonomous first-order...Problem 23E:
In Problems 21-28 find the critical points and phase portrait of the given autonomous first-order...Problem 24E:
In Problems 21-28 find the critical points and phase portrait of the given autonomous first-order...Problem 25E:
In Problems 21-28 find the critical points and phase portrait of the given autonomous first-order...Problem 26E:
In Problems 21-28 find the critical points and phase portrait of the given autonomous first-order...Problem 27E:
In Problems 21-28 find the critical points and phase portrait of the given autonomous first-order...Problem 29E:
In Problems 29 and 30 consider the autonomous differential equation dy/dx =f(y), where the graph of...Problem 30E:
In Problems 29 and 30 consider the autonomous differential equation dy/dx = f(y), where the graph of...Problem 31E:
Consider the autonomous DE dy/dx = (2/)y sin y Determine the critical points of the equation....Problem 32E:
A critical point c of an autonomous first-order DE is said to be isolated if there exists some open...Problem 33E:
Suppose that y(x) is a nonconstant solution of the autonomous equation dy/dx = f(y) and that c is a...Problem 35E:
Using the autonomous equation (2), discuss how it is possible to obtain information about the...Problem 37E:
Suppose the autonomous DE in (2) has no critical points. Discuss the behavior of the solutions.Problem 38E:
Population Model The differential equation in Example 3 is a well-known population model. Suppose...Problem 39E:
Population Model Another population model is given by dpdt=kPh, where h and k are positive...Problem 40E:
Terminal Velocity In Section 1.3 we saw that the autonomous differential equation mdvdt=mgkv, where...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
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A First Course in Differential Equations: The Classic Fifth Edition
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