 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 17823 students have viewed full stepbystep solutions from this chapter.

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

Augmented matrix [A b].
Ax = b is solvable when b is in the column space of A; then [A b] has the same rank as A. Elimination on [A b] keeps equations correct.

Column picture of Ax = b.
The vector b becomes a combination of the columns of A. The system is solvable only when b is in the column space C (A).

Companion matrix.
Put CI, ... ,Cn in row n and put n  1 ones just above the main diagonal. Then det(A  AI) = ±(CI + c2A + C3A 2 + .•. + cnA nl  An).

GaussJordan method.
Invert A by row operations on [A I] to reach [I AI].

Hypercube matrix pl.
Row n + 1 counts corners, edges, faces, ... of a cube in Rn.

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 .

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

Kirchhoff's Laws.
Current Law: net current (in minus out) is zero at each node. Voltage Law: Potential differences (voltage drops) add to zero around any closed loop.

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.

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

Normal matrix.
If N NT = NT N, then N has orthonormal (complex) eigenvectors.

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.

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.

Saddle point of I(x}, ... ,xn ).
A point where the first derivatives of I are zero and the second derivative matrix (a2 II aXi ax j = Hessian matrix) is indefinite.

Schwarz inequality
Iv·wl < IIvll IIwll.Then IvTAwl2 < (vT Av)(wT Aw) for pos def A.

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

Singular Value Decomposition
(SVD) A = U:E VT = (orthogonal) ( diag)( orthogonal) First r columns of U and V are orthonormal bases of C (A) and C (AT), AVi = O'iUi with singular value O'i > O. Last columns are orthonormal bases of nullspaces.

Spanning set.
Combinations of VI, ... ,Vm fill the space. The columns of A span C (A)!

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