Solutions for First Course in Differential Equations (Instructor's)
Problem 1E:
In Problems 122 solve the given differential equation by separation of variables. dydx=sin5xProblem 2E:
In Problems 122 solve the given differential equation by separation of variables. 2. dydx=(x+1)2Problem 3E:
In Problems 122 solve the given differential equation by separation of variables. 3. dx+e3xdy=0Problem 4E:
In Problems 122 solve the given differential equation by separation of variables. 4. dx(y1)2dx=0Problem 5E:
In Problems 122 solve the given differential equation by separation of variables. 5. xdydx=4yProblem 6E:
In Problems 122 solve the given differential equation by separation of variables. 6. dydx+2xy2=0Problem 7E:
In Problems 122 solve the given differential equation by separation of variables. 7. dydx=e3x+2yProblem 8E:
In Problems 122 solve the given differential equation by separation of variables. 8. exydydx=ey+e2xyProblem 10E:
In Problems 122 solve the given differential equation by separation of variables. 10....Problem 11E:
In Problems 122 solve the given differential equation by separation of variables. 11....Problem 12E:
In Problems 122 solve the given differential equation by separation of variables. 12....Problem 13E:
In Problems 122 solve the given differential equation by separation of variables. 13....Problem 14E:
In Problems 122 solve the given differential equation by separation of variables. 14....Problem 15E:
In Problems 122 solve the given differential equation by separation of variables. 15. dSdr=kSProblem 16E:
In Problems 122 solve the given differential equation by separation of variables. 16. dQdt=k(Q70)Problem 17E:
In Problems 122 solve the given differential equation by separation of variables. 17. dpdt=PP2Problem 18E:
In Problems 122 solve the given differential equation by separation of variables. 18. dNdt+N=Ntet+2Problem 19E:
In Problems 122 solve the given differential equation by separation of variables. 19....Problem 20E:
In Problems 122 solve the given differential equation by separation of variables. 20....Problem 21E:
In Problems 122 solve the given differential equation by separation of variables. 21. dydx=x1y2Problem 22E:
In Problems 122 solve the given differential equation by separation of variables. 22. (ex+ex)dydx=y2Problem 23E:
In Problems 2328 find an explicit solution of the given initial-value problem. 23. dxdt=4(x2+1),...Problem 24E:
In Problems 2328 find an explicit solution of the given initial-value problem. 24. dydx=y21x21, y(2)...Problem 25E:
In Problems 2328 find an explicit solution of the given initial-value problem. 25. x2dydx=yxy, y(1)...Problem 26E:
In Problems 2328 find an explicit solution of the given initial-value problem. 26. dydt+2y=1,y(0)=52Problem 28E:
In Problems 2328 find an explicit solution of the given initial-value problem. 28. (1 + x4) dy + x(1...Problem 29E:
In Problems 29 and 30 proceed as in Example 5 and find an explicit solution of the given...Problem 30E:
In Problems 29 and 30 proceed as in Example 5 and find an explicit solution of the given...Problem 31E:
In Problems 3134 find an explicit solution of the given initial-value problem. Determine the exact...Problem 32E:
In Problems 3134 find an explicit solution of the given initial-value problem. Determine the exact...Problem 33E:
In Problems 3134 find an explicit solution of the given initial-value problem. Determine the exact...Problem 34E:
In Problems 3134 find an explicit solution of the given initial-value problem. Determine the exact...Problem 35E:
(a) Find a solution of the initial-value problem consisting of the differential equation in Example...Problem 36E:
Find a solution of xdydx=y2y that passes through the indicated points. (a) (0, 1) (b) (0,.0) (c)...Problem 38E:
Show that an implicit solution of 2xsin2ydx(x2+10)cosydy=0 is given by ln(x2 + 10) + csc y = c. Find...Problem 39E:
Often a radical change in the form of the solution of a differential equation corresponds to a very...Problem 40E:
Often a radical change in the form of the solution of a differential equation corresponds to a very...Problem 41E:
Often a radical change in the form of the solution of a differential equation corresponds to a very...Problem 42E:
Often a radical change in the form of the solution of a differential equation corresponds to a very...Problem 43E:
Every autonomous first-order equation dy/dx = f(y) is separable. Find explicit solutions y1(x),...Problem 44E:
(a) The autonomous first-order differential equation dy/dx = 1/(y 3) has no critical points....Problem 45E:
In Problems 4550 use a technique of integration or a substitution to find an explicit solution of...Problem 46E:
In Problems 4550 use a technique of integration or a substitution to find an explicit solution of...Problem 47E:
In Problems 4550 use a technique of integration or a substitution to find an explicit solution of...Problem 48E:
In Problems 4550 use a technique of integration or a substitution to find an explicit solution of...Problem 49E:
In Problems 4550 use a technique of integration or a substitution to find an explicit solution of...Problem 50E:
In Problems 4550 use a technique of integration or a substitution to find an explicit solution of...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
We offer sample solutions for First Course in Differential Equations (Instructor's) homework problems. See examples below:
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A First Course in Differential Equations: The Classic Fifth Edition
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A First Course in Differential Equations with Modeling Applications
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