 8.3.1: For 116, determine the annihilator of the given function.. F(x) = 5...
 8.3.2: For 116, determine the annihilator of the given function.F(x) = 2ex...
 8.3.3: For 116, determine the annihilator of the given function.F(x) = sin...
 8.3.4: For 116, determine the annihilator of the given function.F(x) = x3e...
 8.3.5: For 116, determine the annihilator of the given function.F(x) = 4e2...
 8.3.6: For 116, determine the annihilator of the given function.F(x) = ex ...
 8.3.7: For 116, determine the annihilator of the given function.
 8.3.8: For 116, determine the annihilator of the given function.
 8.3.9: For 116, determine the annihilator of the given function.
 8.3.10: For 116, determine the annihilator of the given function.F(x) = e4x...
 8.3.11: For 116, determine the annihilator of the given function.
 8.3.12: For 116, determine the annihilator of the given function.F(x) = x c...
 8.3.13: For 116, determine the annihilator of the given function.F(x) = cos...
 8.3.14: For 116, determine the annihilator of the given function.F(x) = sin...
 8.3.15: For 116, determine the annihilator of the given function.F(x) = sin...
 8.3.16: For 116, determine the annihilator of the given function.F(x) = sin...
 8.3.17: For 1732, determine the general solution to the given differential ...
 8.3.18: For 1732, determine the general solution to the given differential ...
 8.3.19: For 1732, determine the general solution to the given differential ...
 8.3.20: For 1732, determine the general solution to the given differential ...
 8.3.21: For 1732, determine the general solution to the given differential ...
 8.3.22: For 1732, determine the general solution to the given differential ...
 8.3.23: For 1732, determine the general solution to the given differential ...
 8.3.24: For 1732, determine the general solution to the given differential ...
 8.3.25: For 1732, determine the general solution to the given differential ...
 8.3.26: For 1732, determine the general solution to the given differential ...
 8.3.27: For 1732, determine the general solution to the given differential ...
 8.3.28: For 1732, determine the general solution to the given differential ...
 8.3.29: For 1732, determine the general solution to the given differential ...
 8.3.30: For 1732, determine the general solution to the given differential ...
 8.3.31: For 1732, determine the general solution to the given differential ...
 8.3.32: For 1732, determine the general solution to the given differential ...
 8.3.33: For 3337, solve the given initialvalue problem:y + 9y = 5 cos 2x, ...
 8.3.34: For 3337, solve the given initialvalue problem:
 8.3.35: For 3337, solve the given initialvalue problem:y + y 2y = 10 sin x...
 8.3.36: For 3337, solve the given initialvalue problem:(D2 + D 2)y = 4 cos...
 8.3.37: For 3337, solve the given initialvalue problem:(D 1)(D 2)(D 3)y = ...
 8.3.38: At time t the displacement from equilibrium, y(t), ofan undamped sp...
 8.3.39: For 3947, determine an appropriate trial solution for the given dif...
 8.3.40: For 3947, determine an appropriate trial solution for the given dif...
 8.3.41: For 3947, determine an appropriate trial solution for the given dif...
 8.3.42: For 3947, determine an appropriate trial solution for the given dif...
 8.3.43: For 3947, determine an appropriate trial solution for the given dif...
 8.3.44: For 3947, determine an appropriate trial solution for the given dif...
 8.3.45: For 3947, determine an appropriate trial solution for the given dif...
 8.3.46: For 3947, determine an appropriate trial solution for the given dif...
 8.3.47: For 3947, determine an appropriate trial solution for the given dif...
 8.3.48: Derive an appropriate trial solution for the differential equation ...
Solutions for Chapter 8.3: The Method of Undetermined Coefficients: Annihilators
Full solutions for Differential Equations  4th Edition
ISBN: 9780321964670
Solutions for Chapter 8.3: The Method of Undetermined Coefficients: Annihilators
Get Full SolutionsChapter 8.3: The Method of Undetermined Coefficients: Annihilators includes 48 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Differential Equations, edition: 4. Differential Equations was written by and is associated to the ISBN: 9780321964670. Since 48 problems in chapter 8.3: The Method of Undetermined Coefficients: Annihilators have been answered, more than 9838 students have viewed full stepbystep solutions from this chapter.

Commuting matrices AB = BA.
If diagonalizable, they share n eigenvectors.

Condition number
cond(A) = c(A) = IIAIlIIAIII = amaxlamin. In Ax = b, the relative change Ilox III Ilx II is less than cond(A) times the relative change Ilob III lib II· Condition numbers measure the sensitivity of the output to change in the input.

Dot product = Inner product x T y = XI Y 1 + ... + Xn Yn.
Complex dot product is x T Y . Perpendicular vectors have x T y = O. (AB)ij = (row i of A)T(column j of B).

Fibonacci numbers
0,1,1,2,3,5, ... satisfy Fn = Fnl + Fn 2 = (A7 A~)I()q A2). Growth rate Al = (1 + .J5) 12 is the largest eigenvalue of the Fibonacci matrix [ } A].

GramSchmidt orthogonalization A = QR.
Independent columns in A, orthonormal columns in Q. Each column q j of Q is a combination of the first j columns of A (and conversely, so R is upper triangular). Convention: diag(R) > o.

Graph G.
Set of n nodes connected pairwise by m edges. A complete graph has all n(n  1)/2 edges between nodes. A tree has only n  1 edges and no closed loops.

Hankel matrix H.
Constant along each antidiagonal; hij depends on i + j.

Hermitian matrix A H = AT = A.
Complex analog a j i = aU of a symmetric matrix.

Indefinite matrix.
A symmetric matrix with eigenvalues of both signs (+ and  ).

Inverse matrix AI.
Square matrix with AI A = I and AAl = I. No inverse if det A = 0 and rank(A) < n and Ax = 0 for a nonzero vector x. The inverses of AB and AT are B1 AI and (AI)T. Cofactor formula (Al)ij = Cji! detA.

Lucas numbers
Ln = 2,J, 3, 4, ... satisfy Ln = L n l +Ln 2 = A1 +A~, with AI, A2 = (1 ± /5)/2 from the Fibonacci matrix U~]' Compare Lo = 2 with Fo = O.

Nullspace matrix N.
The columns of N are the n  r special solutions to As = O.

Pascal matrix
Ps = pascal(n) = the symmetric matrix with binomial entries (i1~;2). Ps = PL Pu all contain Pascal's triangle with det = 1 (see Pascal in the index).

Permutation matrix P.
There are n! orders of 1, ... , n. The n! P 's have the rows of I in those orders. P A puts the rows of A in the same order. P is even or odd (det P = 1 or 1) based on the number of row exchanges to reach I.

Projection matrix P onto subspace S.
Projection p = P b is the closest point to b in S, error e = b  Pb is perpendicularto S. p 2 = P = pT, eigenvalues are 1 or 0, eigenvectors are in S or S...L. If columns of A = basis for S then P = A (AT A) 1 AT.

Rotation matrix
R = [~ CS ] rotates the plane by () and R 1 = RT rotates back by (). Eigenvalues are eiO and eiO , eigenvectors are (1, ±i). c, s = cos (), sin ().

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

Subspace S of V.
Any vector space inside V, including V and Z = {zero vector only}.

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.

Triangle inequality II u + v II < II u II + II v II.
For matrix norms II A + B II < II A II + II B II·