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Fundamentals of Differential Equations [With CDROM] - 7th Edition
7th Edition
ISBN: 9780321410481
Author: Saff, Edward B., Snider, Arthur David, Nagle, R. Kent
Publisher: Addison Wesley
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Textbook Question
Chapter 6.3, Problem 5E
In Problems 5-10, find a general solution to the given equation.
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A factorization A = PDP 1 is not unique. For A=
7 2
-4 1
1
1
5 0
2
1
one factorization is P =
D=
and P-1
30
=
Use this information with D₁
=
to find a matrix P₁ such that
-
-1 -2
0 3
1
-
- 1
05
A-P,D,P
P1
(Type an integer or simplified fraction for each matrix element.)
Matrix A is factored in the form PDP 1. Use the Diagonalization Theorem to find the eigenvalues of A and a basis for each eigenspace.
30 -1
-
1 0 -1
400
0
0 1
A=
3 4 3
0 1 3
040
3 1 3
0 0
4
1
0
0
003
-1 0 -1
Select the correct choice below and fill in the answer boxes to complete your choice.
(Use a comma to separate vectors as needed.)
A basis for the corresponding eigenspace is {
A. There is one distinct eigenvalue, λ =
B. In ascending order, the two distinct eigenvalues are λ₁
...
=
and 2
=
Bases for the corresponding eigenspaces are {
and ( ), respectively.
C. In ascending order, the three distinct eigenvalues are λ₁ =
=
12/2
=
and 3 = Bases for the corresponding eigenspaces are
{}, }, and {
respectively.
N Page
0.6.
0.4.
0.2-
-0.2-
-0.4-
-6.6
-5
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10
Chapter 6 Solutions
Fundamentals of Differential Equations [With CDROM] - 7th Edition
Ch. 6.1 - In Problems 1-6, determine the largest interval...Ch. 6.1 - In Problems 1-6, determine the largest interval...Ch. 6.1 - In Problems 1-6, determine the largest interval...Ch. 6.1 - In Problems 1-6, determine the largest interval...Ch. 6.1 - In Problems 1-6, determine the largest interval...Ch. 6.1 - In Problems 1-6, determine the largest interval...Ch. 6.1 - Prob. 7ECh. 6.1 - In Problems7-14, determine whether the given...Ch. 6.1 - In Problems7-14, determine whether the given...Ch. 6.1 - In Problems7-14, determine whether the given...
Ch. 6.1 - In Problems7-14, determine whether the given...Ch. 6.1 - In Problems7-14, determine whether the given...Ch. 6.1 - In Problems7-14, determine whether the given...Ch. 6.1 - In Problems7-14, determine whether the given...Ch. 6.1 - Using the Wronskian in Problems 15-18, verify that...Ch. 6.1 - Prob. 16ECh. 6.1 - Prob. 17ECh. 6.1 - Prob. 18ECh. 6.1 - In Problems 19-22, a particular solution and a...Ch. 6.1 - In Problems 19-22, a particular solution and a...Ch. 6.1 - In Problems 19-22, a particular solution and a...Ch. 6.1 - In Problems 19-22, a particular solution and a...Ch. 6.1 - Let L[y]:=y+y+xy, y1(x):=sinx, and y2(x):=x....Ch. 6.1 - Let L[y]:=yxy+4y3xy", y1(x)=cos2x, and y2(x):=1/3....Ch. 6.1 - Prob. 25ECh. 6.1 - Prob. 26ECh. 6.1 - Prob. 27ECh. 6.1 - Prob. 28ECh. 6.1 - Prob. 29ECh. 6.1 - Prob. 30ECh. 6.1 - Prob. 31ECh. 6.1 - Prob. 32ECh. 6.1 - Prob. 33ECh. 6.1 - Prob. 34ECh. 6.1 - Prob. 35ECh. 6.2 - In Problems 1-14, find a general solution for the...Ch. 6.2 - Prob. 2ECh. 6.2 - In Problems 1-14, find a general solution for the...Ch. 6.2 - Prob. 4ECh. 6.2 - Prob. 5ECh. 6.2 - Prob. 6ECh. 6.2 - Prob. 7ECh. 6.2 - Prob. 8ECh. 6.2 - Prob. 9ECh. 6.2 - Prob. 10ECh. 6.2 - Prob. 11ECh. 6.2 - Prob. 12ECh. 6.2 - Prob. 13ECh. 6.2 - In Problems 1-14, find a general solution for the...Ch. 6.2 - In Problems 15-18, find a general solution to the...Ch. 6.2 - Prob. 16ECh. 6.2 - In Problems 15 18, find a general solution to the...Ch. 6.2 - Prob. 18ECh. 6.2 - Prob. 19ECh. 6.2 - In Problems 1921, solve the given initial value...Ch. 6.2 - Prob. 21ECh. 6.2 - Prob. 22ECh. 6.2 - In Problems 22 and 23, find a general solution for...Ch. 6.2 - Prob. 24ECh. 6.2 - Prob. 25ECh. 6.2 - Prob. 26ECh. 6.2 - Prob. 27ECh. 6.2 - Find a general solution to y3yy=0 by using Newtons...Ch. 6.2 - Prob. 29ECh. 6.2 - Prob. 30ECh. 6.2 - Higher-Order Cauchy-Euler Equations. A...Ch. 6.2 - Prob. 32ECh. 6.2 - On a smooth horizontal surface, a mass of m1 kg is...Ch. 6.2 - Suppose the two springs in the coupled mass-spring...Ch. 6.2 - Vibrating Beam. In studying the transverse...Ch. 6.3 - In Problems 1-4, use the method of undetermined...Ch. 6.3 - Prob. 2ECh. 6.3 - Prob. 3ECh. 6.3 - Prob. 4ECh. 6.3 - In Problems 5-10, find a general solution to the...Ch. 6.3 - In Problems 5-10, find a general solution to the...Ch. 6.3 - Prob. 7ECh. 6.3 - Prob. 8ECh. 6.3 - Prob. 9ECh. 6.3 - In Problems 5-10, find a general solution to the...Ch. 6.3 - In Problems 11-20, find a differential operator...Ch. 6.3 - In Problems 11-20, find a differential operator...Ch. 6.3 - In Problems 11-20, find a differential operator...Ch. 6.3 - In Problems 11-20, find a differential operator...Ch. 6.3 - In Problems 11-20, find a differential operator...Ch. 6.3 - In Problems 11-20, find a differential operator...Ch. 6.3 - In Problems 11-20, find a differential operator...Ch. 6.3 - In Problems 11-20, find a differential operator...Ch. 6.3 - In Problems 11-20, find a differential operator...Ch. 6.3 - In Problems 11-20, find a differential operator...Ch. 6.3 - In Problems 21-30, use the annihilator method to...Ch. 6.3 - In Problems 21-30, use the annihilator method to...Ch. 6.3 - In Problems 21-30, use the annihilator method to...Ch. 6.3 - In Problems 21-30, use the annihilator method to...Ch. 6.3 - In Problems 21-30, use the annihilator method to...Ch. 6.3 - In Problems 21-30, use the annihilator method to...Ch. 6.3 - In Problems 21-30, use the annihilator method to...Ch. 6.3 - Prob. 28ECh. 6.3 - Prob. 29ECh. 6.3 - In Problems 21-30, use the annihilator method to...Ch. 6.3 - Prob. 31ECh. 6.3 - Prob. 32ECh. 6.3 - In Problems 31-33, solve the given initial value...Ch. 6.3 - Prob. 34ECh. 6.3 - Prob. 35ECh. 6.3 - Use the annihilator method to show that if f(x) in...Ch. 6.3 - Prob. 37ECh. 6.3 - In Problems 38 and 39, use the elimination method...Ch. 6.3 - Prob. 39ECh. 6.4 - In Problems 1-6, use the method of variation of...Ch. 6.4 - Prob. 2ECh. 6.4 - In Problems 1-6, use the method of variation of...Ch. 6.4 - Prob. 4ECh. 6.4 - Prob. 5ECh. 6.4 - In Problems 1-6, use the method of variation of...Ch. 6.4 - Prob. 7ECh. 6.4 - Prob. 8ECh. 6.4 - Prob. 9ECh. 6.4 - Given that {x,x1,x4} is a fundamental solution set...Ch. 6.4 - Prob. 11ECh. 6.4 - Prob. 12ECh. 6.4 - Prob. 13ECh. 6.4 - Prob. 14ECh. 6.RP - Determine the intervals for which Theorem 1 on...Ch. 6.RP - Determine whether the given functions are linearly...Ch. 6.RP - Show that the set of functions...Ch. 6.RP - Find a general solution for the given differential...Ch. 6.RP - Find a general solution for the homogeneous linear...Ch. 6.RP - Prob. 6RPCh. 6.RP - Prob. 7RPCh. 6.RP - Use the annihilator method to determine the form...Ch. 6.RP - Find a general solution to the Cauchy-Euler...Ch. 6.RP - Find a general solution to the given Cauchy-Euler...
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