Solutions for First Course in Differential Equations (Instructor's)
Problem 1RE:
In Problems 1 and 2 fill in the blank and then write this result as a linear first-order...Problem 2RE:
In Problems 1 and 2 fill in the blank and then write this result as a linear first-order...Problem 3RE:
In Problems 3 and 4 fill in the blank and then write this result as a linear second-order...Problem 4RE:
In Problems 3 and 4 fill in the blank and then write this result as a linear second-order...Problem 5RE:
In Problems 5 and 6 compute y and y and then combine these derivatives with y as a linear...Problem 6RE:
In Problems 5 and 6 compute y and y and then combine these derivatives with y as a linear...Problem 7RE:
In Problems 712 match each of the given differential equations with one or more of these solutions:...Problem 8RE:
In Problems 712 match each of the given differential equations with one or more of these solutions:...Problem 9RE:
In Problems 712 match each of the given differential equations with one or more of these solutions:...Problem 10RE:
In Problems 712 match each of the given differential equations with one or more of these solutions:...Problem 11RE:
In Problems 712 match each of the given differential equations with one or more of these solutions:...Problem 12RE:
In Problems 712 match each of the given differential equations with one or more of these solutions:...Problem 13RE:
In Problems 13 and 14 determine by inspection at least one solution of the given differential...Problem 14RE:
In Problems 13 and 14 determine by inspection at least one solution of the given differential...Problem 15RE:
In Problems 15 and 16 interpret each statement as a differential equation. 15. On the graph of y =...Problem 16RE:
In Problems 15 and 16 interpret each statement as a differential equation. 16. On the graph of y =...Problem 17RE:
(a) Give the domain of the function y = x2/3. (b) Give the largest interval I of definition over...Problem 18RE:
(a) Verify that the one-parameter family y2 2y = x2 x + c is an implicit solution of the...Problem 19RE:
The function y = x 2/x is a solution of the DE xy + y = 2x. Find x0 and the largest interval I for...Problem 20RE:
Suppose that y(x) denotes a solution of the first-order IVP y = x2 + y2, y(1) = 1 and that y(x)...Problem 21RE:
A differential equation may possess more than one family of solutions. (a) Plot different members of...Problem 22RE:
What is the slope of the tangent line to the graph of a solution of y=6y+5x3 that passes through (1,...Problem 23RE:
In Problems 2326 verify that the indicated function is an explicit solution of the given...Problem 24RE:
In Problems 2326 verify that the indicated function is an explicit solution of the given...Problem 25RE:
In Problems 2326 verify that the indicated function is an explicit solution of the given...Problem 26RE:
In Problems 2326 verify that the indicated function is an explicit solution of the given...Problem 27RE:
In Problems 2730 use (12) of Section 1.1 to verify that the indicated function is a solution of the...Problem 28RE:
In Problems 2730 use (12) of Section 1.1 to verify that the indicated function is a solution of the...Problem 29RE:
In Problems 2730 use (12) of Section 1.1 to verify that the indicated function is a solution of the...Problem 30RE:
In Problems 2730 use (12) of Section 1.1 to verify that the indicated function is a solution of the...Problem 31RE:
In Problems 3134 verify that the indicated expression is an implicit solution of the given...Problem 32RE:
In Problems 3134 verify that the indicated expression is an implicit solution of the given...Problem 33RE:
In Problems 3134 verify that the indicated expression is an implicit solution of the given...Problem 34RE:
In Problems 3134 verify that the indicated expression is an implicit solution of the given...Problem 35RE:
In Problems 3538, y = c1e3x + c2ex 2x is a two-parameter family of the second-order DE y 2y 3y =...Problem 36RE:
In Problems 3538, y = c1e3x + c2ex 2x is a two-parameter family of the second-order DE y 2y 3y =...Problem 37RE:
In Problems 3538, y = c1e3x + c2ex 2x is a two-parameter family of the second-order DE y 2y 3y =...Problem 38RE:
In Problems 3538, y = c1e3x + c2ex 2x is a two-parameter family of the second-order DE y 2y 3y =...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
Sample Solutions for this Textbook
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A First Course in Differential Equations: The Classic Fifth Edition
5th Edition
ISBN: 9780534373887
A First Course in Differential Equations with Modeling Applications
12th Edition
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