Differential Equations And Linear Algeb...4th EditionStephen W. Goode, Scott A. Annin Publisher: Pearson (edition 4)ISBN: 9780321985811
Differential Equations And Linear Algeb...
Solutions for Differential Equations And Linear Algebra, Books A La Carte Edition (4th Edition)
Problem 1TFR:
True-False review For items a-n, decide if the given statement is true or false, and give a brief...Problem 5P:
Verify that, for t0, y(t)=lnt is a solution to the differential equation 2(dydx)3=d3ydt3.Problem 6P:
Verify that y(x)=x/(x+1) is a solution to the differential equation y+d2ydx2=dydx+x3+2x23(1+x)3.Problem 8P:
By writing Equation 1.1.7 in the form 1TTmdTdt=k and using u1dudt=ddt(lnu), derive 1.1.8.Problem 9P:
A glass of water whose temperature is 50F is taken outside at noon on a day whose temperature is...Problem 10P:
On a cold winter day (10F), an object is brought outside from a 70F room. If it takes 40 minutes for...Problem 11P:
For Problems 11-16, find the equation of the orthogonal trajectories to the given family of curves....Problem 12P:
For Problems 11-16, find the equation of the orthogonal trajectories to the given family of curves....Problem 13P:
For Problems 11-16, find the equation of the orthogonal trajectories to the given family of curves....Problem 14P:
For Problems 11-16, find the equation of the orthogonal trajectories to the given family of curves....Problem 15P:
For Problems 11-16, find the equation of the orthogonal trajectories to the given family of curves....Problem 16P:
For Problems 11-16, find the equation of the orthogonal trajectories to the given family of curves....Problem 17P:
For problems 17-20, m denotes a fixed nonzero constant, and c is the constant distinguishing the...Problem 18P:
For problems 17-20, m denotes a fixed nonzero constant, and c is the constant distinguishing the...Problem 19P:
For problems 17-20, m denotes a fixed nonzero constant, and c is the constant distinguishing the...Problem 20P:
For problems 17-20, m denotes a fixed nonzero constant, and c is the constant distinguishing the...Problem 21P:
Consider the family of circles x2+y2=2cx. Show that the differential equation for determining the...Problem 22P:
We call a coordinate system (u,v) orthogonal if its coordinate curves the two family of curves...Problem 23P:
Any curve with the property that whenever it intersects a curve of a given family it does so at an...Problem 24P:
An object is released from rest at a height of 100 meters above the ground. Neglecting frictional...Problem 25P:
A five-foot-tall boy tosses a tennis ball straight up from the level of the top of his head....Problem 26P:
A pyrotechnic rocket is to be launched vertically upwards from the ground. For optimal viewing, the...Problem 27P:
Repeat Problem 26 under the assumption that the rocket is launched from a platform five meters above...Problem 29P:
An object that is released from a height h meters above the ground with a vertical velocity of v0...Problem 30P:
Verify that y(t)=Acos(t) is a solution to the differential equation 1.1.21, where A and are nonzero...Problem 31P:
Verify that y(t)=c1cost+c2sint is a solution to the differential equation 1.1.21. Show that the...Browse All Chapters of This Textbook
Chapter 1.1 - Differential Equations EverywhereChapter 1.2 - Basic Ideas And TerminologyChapter 1.3 - The Geometry Of First-order Differential EquationsChapter 1.4 - Separable Differential EquationsChapter 1.5 - Some Simple Population ModelsChapter 1.6 - First-order Linear Differential EquationsChapter 1.7 - Modeling Problems Using First-order Linear Differential EquationsChapter 1.8 - Change Of VariablesChapter 1.9 - Exact Differential EquationsChapter 1.10 - Numerical Solution To First-order Differential Equations
Chapter 1.11 - Some Higher-order Differential EquationsChapter 1.12 - Chapter ReviewChapter 2.1 - Matrices: Definitions And NotationChapter 2.2 - Matrix AlgebraChapter 2.3 - Terminology For Systems Of Linear EquationsChapter 2.4 - Row-echelon Matrices And Elementary Row OperationsChapter 2.5 - Gaussian EliminationChapter 2.6 - The Inverse Of A Square MatrixChapter 2.7 - Elementary Matrices And The Lu FactorizationChapter 2.8 - The Invertible Matrix Theorem IChapter 2.9 - Chapter ReviewChapter 3.1 - The Definition Of The DeterminantChapter 3.2 - Properties Of DeterminantsChapter 3.3 - Cofactor ExpansionsChapter 3.4 - Summary Of DeterminantsChapter 3.5 - Chapter ReviewChapter 4.1 - Vectors In R.nChapter 4.2 - Definition Of A Vector SpaceChapter 4.3 - SubspacesChapter 4.4 - Spanning SetsChapter 4.5 - Linear Dependence And Linear IndependenceChapter 4.6 - Bases And DimensionChapter 4.7 - Change Of BasisChapter 4.8 - Row Space And Column SpaceChapter 4.9 - The Rank-nullity TheoremChapter 4.11 - Chapter ReviewChapter 5.1 - Definition Of An Inner Product SpaceChapter 5.2 - Orthogonal Sets Of Vectors And Orthogonal ProjectionsChapter 5.3 - The Gram-schmidt ProcessChapter 5.4 - Least Squares ApproximationChapter 5.5 - Chapter ReviewChapter 6.1 - Definition Of A Linear TransformationChapter 6.2 - Transformations Of R.2Chapter 6.3 - The Kernel And Range Of A Linear TransformationChapter 6.4 - Additional Properties Of Linear TransformationsChapter 6.5 - The Matrix Of A Linear TransformationChapter 6.6 - Chapter ReviewChapter 7.1 - The Eigenvalue/eigenvector ProblemChapter 7.2 - General Results For Eigenvalues And EigenvectorsChapter 7.3 - DiagonalizationChapter 7.4 - An Introduction To The Matrix Exponential FunctionChapter 7.5 - Orthogonal Diagonalization And Quadratic FormsChapter 7.6 - Jordan Canonical FormsChapter 7.7 - Chapter ReviewChapter 8.1 - General Theory For Linear Differential EquationsChapter 8.2 - Constant Coefficient Homogeneous Linear Differential EquationsChapter 8.3 - The Method Of Undetermined Coefficients: AnnihilatorsChapter 8.5 - Oscillations Of A Mechanical SystemChapter 8.6 - Rlc CircuitsChapter 8.7 - The Variation Of Parameters MethodChapter 8.8 - A Differential Equation With Nonconstant CoefficientsChapter 8.9 - Reduction Of OrderChapter 8.10 - Chapter ReviewChapter 9.1 - First-order Linear SystemsChapter 9.2 - Vector FormulationChapter 9.3 - General Results For First-order Linear Differential SystemsChapter 9.4 - Vector Differential Equations: Nondefective Coefficient MatrixChapter 9.5 - Vector Differential Equations: Defective Coefficient MatrixChapter 9.6 - Variation-of-parameters For Linear SystemsChapter 9.7 - Some Applications Of Linear Systems Of Differential EquationsChapter 9.8 - Matrix Exponential Function And Systems Of Differential EquationsChapter 9.9 - The Phase Plane For Linear Autonomous SystemsChapter 9.10 - Nonlinear SystemsChapter 9.11 - Chapter ReviewChapter 10.1 - Definition Of The Laplace TransformChapter 10.2 - The Existence Of The Laplace Transform And The Inverse TransformChapter 10.3 - Periodic Functions And The Laplace TransformChapter 10.4 - The Transform Of Derivatives And Solution Of Initial-value ProblemsChapter 10.5 - The First Shifting TheoremChapter 10.6 - The Unit Step FunctionChapter 10.7 - The Second Shifting TheoremChapter 10.8 - Impulsive Driving Terms: The Dirac Delta FunctionChapter 10.9 - The Convolution IntegralChapter 10.10 - Chapter ReviewChapter 11.1 - A Review Of Power SeriesChapter 11.2 - Series Solutions About An Ordinary PointChapter 11.3 - The Legendre EquationChapter 11.4 - Series Solutions About A Regular Singular PointChapter 11.5 - Frobenius TheoryChapter 11.6 - Bessel's Equation Of Order PChapter 11.7 - Chapter ReviewChapter A - Review Of Complex NumbersChapter B - Review Of Partial FractionsChapter C - Review Of Integration Techniques
Sample Solutions for this Textbook
We offer sample solutions for Differential Equations And Linear Algebra, Books A La Carte Edition (4th Edition) homework problems. See examples below:
Chapter 1.12, Problem 1APChapter 2.9, Problem 1APChapter 3.5, Problem 1APChapter 4.11, Problem 1APChapter 5.5, Problem 1APGiven: The given mapping is, T:ℝ2→ℝ4 defined by T(x,y)=(x+y,0,x−y,xy). Approach: The following...Given: The given matrix A is, A=[3016−1] Approach: An n×n matrix that is similar to a diagonal...Chapter 8.10, Problem 1APChapter 9.11, Problem 1AP
Given: A function f is defined on an interval [0,∞) as, f(t)=3t−4 Approach: The function F(s) is...Chapter 11.7, Problem 1APGiven: The given complex number is, z=2+5i Approach: The definition of complex conjugate states...Given: The given rational function is, 2x−1(x+1)(x+2). Approach: The standard way to find the...The given integral is, ∫xcosxdx Approach: Integration by parts: the basic formula for integration by...
More Editions of This Book
Corresponding editions of this textbook are also available below:
Differential Equations & Linear Algebra 3e
3rd Edition
ISBN: 9781292025131
Differential Equations And Linear Algebra
3rd Edition
ISBN: 9780130457943
Differential Equations and Linear Algebra (4th Edition)
4th Edition
ISBN: 9780321964670
EBK DIFFERENTIAL EQUATIONS AND LINEAR A
4th Edition
ISBN: 9780321990167
EBK DIFFERENTIAL EQUATIONS AND LINEAR A
4th Edition
ISBN: 8220102019799
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