 4.7.4.1.288: In 118 solve the given differential equation.x2y 2y 0
 4.7.4.1.289: In 118 solve the given differential equation.4x2y y 0
 4.7.4.1.290: In 118 solve the given differential equation.xy y 0 4
 4.7.4.1.291: In 118 solve the given differential equation.xy 3y 0
 4.7.4.1.292: In 118 solve the given differential equation.x2y xy 4y 0 6
 4.7.4.1.293: In 118 solve the given differential equation.x2y 5xy 3y 0
 4.7.4.1.294: In 118 solve the given differential equation.x2y 3xy 2y 0 8
 4.7.4.1.295: In 118 solve the given differential equation.x2y 3xy 4y 0
 4.7.4.1.296: In 118 solve the given differential equation.25x2y 25xy y 0 1
 4.7.4.1.297: In 118 solve the given differential equation.4x2y 4xy y 0
 4.7.4.1.298: In 118 solve the given differential equation.x2y 5xy 4y 0 1
 4.7.4.1.299: In 118 solve the given differential equation.x2y 8xy 6y 0
 4.7.4.1.300: In 118 solve the given differential equation.3x2y 6xy y 0 1
 4.7.4.1.301: In 118 solve the given differential equation.x2y 7xy 41y 0
 4.7.4.1.302: In 118 solve the given differential equation.x3y 6y 0
 4.7.4.1.303: In 118 solve the given differential equation.x3y xy y 0
 4.7.4.1.304: In 118 solve the given differential equation.xy(4) 6y 0
 4.7.4.1.305: In 118 solve the given differential equation.x4y(4) 6x3y 9x2y 3xy y 0
 4.7.4.1.306: In 1924 solve the given differential equation by variation of param...
 4.7.4.1.307: In 1924 solve the given differential equation by variation of param...
 4.7.4.1.308: In 1924 solve the given differential equation by variation of param...
 4.7.4.1.309: In 1924 solve the given differential equation by variation of param...
 4.7.4.1.310: In 1924 solve the given differential equation by variation of param...
 4.7.4.1.311: In 1924 solve the given differential equation by variation of param...
 4.7.4.1.312: In 2530 solve the given initialvalue problem. Use a graphing utili...
 4.7.4.1.313: In 2530 solve the given initialvalue problem. Use a graphing utili...
 4.7.4.1.314: In 2530 solve the given initialvalue problem. Use a graphing utili...
 4.7.4.1.315: In 2530 solve the given initialvalue problem. Use a graphing utili...
 4.7.4.1.316: In 2530 solve the given initialvalue problem. Use a graphing utili...
 4.7.4.1.317: In 2530 solve the given initialvalue problem. Use a graphing utili...
 4.7.4.1.318: In 3136 use the substitution x et to transform the given CauchyEul...
 4.7.4.1.319: In 3136 use the substitution x et to transform the given CauchyEul...
 4.7.4.1.320: In 3136 use the substitution x et to transform the given CauchyEul...
 4.7.4.1.321: In 3136 use the substitution x et to transform the given CauchyEul...
 4.7.4.1.322: In 3136 use the substitution x et to transform the given CauchyEul...
 4.7.4.1.323: In 3136 use the substitution x et to transform the given CauchyEul...
 4.7.4.1.324: In 37 and 38 use the substitution to solve the given initialvalue ...
 4.7.4.1.325: In 37 and 38 use the substitution to solve the given initialvalue ...
 4.7.4.1.326: In 39 and 40 use to solve the given differential equation.(x 3)2 y ...
 4.7.4.1.327: In 39 and 40 use to solve the given differential equation.(x 1)2y (...
 4.7.4.1.328: In 41 and 42 use the substitution to solve the given differential e...
 4.7.4.1.329: In 41 and 42 use the substitution to solve the given differential e...
 4.7.4.1.330: Give the largest interval over which the general solution of is def...
 4.7.4.1.331: Can a CauchyEuler differential equation of lowest order with real ...
 4.7.4.1.332: The initialconditions y(0) y0, y(0) y1 apply to each of the follow...
 4.7.4.1.333: What are the xintercepts of the solution curve shown in Figure 4.7...
 4.7.4.1.334: In 4750 solve the given differential equation by using a CAS to fin...
 4.7.4.1.335: In 4750 solve the given differential equation by using a CAS to fin...
 4.7.4.1.336: In 4750 solve the given differential equation by using a CAS to fin...
 4.7.4.1.337: In 4750 solve the given differential equation by using a CAS to fin...
 4.7.4.1.338: Solve x3y x2y 2xy 6y x2 by variation of parameters. Use a CAS as an...
Solutions for Chapter 4.7: HigherOrder Differential Equations
Full solutions for Differential Equations with BoundaryValue Problems,  8th Edition
ISBN: 9781111827069
Solutions for Chapter 4.7: HigherOrder Differential Equations
Get Full SolutionsChapter 4.7: HigherOrder Differential Equations includes 51 full stepbystep solutions. Since 51 problems in chapter 4.7: HigherOrder Differential Equations have been answered, more than 21243 students have viewed full stepbystep solutions from this chapter. Differential Equations with BoundaryValue Problems, was written by and is associated to the ISBN: 9781111827069. This textbook survival guide was created for the textbook: Differential Equations with BoundaryValue Problems,, edition: 8. This expansive textbook survival guide covers the following chapters and their solutions.

Associative Law (AB)C = A(BC).
Parentheses can be removed to leave ABC.

Diagonal matrix D.
dij = 0 if i # j. Blockdiagonal: zero outside square blocks Du.

Fundamental Theorem.
The nullspace N (A) and row space C (AT) are orthogonal complements in Rn(perpendicular from Ax = 0 with dimensions rand n  r). Applied to AT, the column space C(A) is the orthogonal complement of N(AT) in Rm.

Hilbert matrix hilb(n).
Entries HU = 1/(i + j 1) = Jd X i 1 xj1dx. Positive definite but extremely small Amin and large condition number: H is illconditioned.

Incidence matrix of a directed graph.
The m by n edgenode incidence matrix has a row for each edge (node i to node j), with entries 1 and 1 in columns i and j .

Markov matrix M.
All mij > 0 and each column sum is 1. Largest eigenvalue A = 1. If mij > 0, the columns of Mk approach the steady state eigenvector M s = s > O.

Multiplication Ax
= Xl (column 1) + ... + xn(column n) = combination of columns.

Pivot columns of A.
Columns that contain pivots after row reduction. These are not combinations of earlier columns. The pivot columns are a basis for the column space.

Plane (or hyperplane) in Rn.
Vectors x with aT x = O. Plane is perpendicular to a =1= O.

Random matrix rand(n) or randn(n).
MATLAB creates a matrix with random entries, uniformly distributed on [0 1] for rand and standard normal distribution for randn.

Rank r (A)
= number of pivots = dimension of column space = dimension of row space.

Reflection matrix (Householder) Q = I 2uuT.
Unit vector u is reflected to Qu = u. All x intheplanemirroruTx = o have Qx = x. Notice QT = Q1 = Q.

Right inverse A+.
If A has full row rank m, then A+ = AT(AAT)l has AA+ = 1m.

Similar matrices A and B.
Every B = MI AM has the same eigenvalues as A.

Skewsymmetric matrix K.
The transpose is K, since Kij = Kji. Eigenvalues are pure imaginary, eigenvectors are orthogonal, eKt is an orthogonal matrix.

Spectrum of A = the set of eigenvalues {A I, ... , An}.
Spectral radius = max of IAi I.

Symmetric factorizations A = LDLT and A = QAQT.
Signs in A = signs in D.

Symmetric matrix A.
The transpose is AT = A, and aU = a ji. AI is also symmetric.

Transpose matrix AT.
Entries AL = Ajj. AT is n by In, AT A is square, symmetric, positive semidefinite. The transposes of AB and AI are BT AT and (AT)I.

Wavelets Wjk(t).
Stretch and shift the time axis to create Wjk(t) = woo(2j t  k).