Consider initial value problem -6 k j' j, j(0) = Jo, k 1 where k is a real parameter. a. Determine all values of k for which the coefficient matrix has distinct real eigenvalues. Enter NONE if there are no values of k for which the coefficient matrix has distinct real eigenvalues. -7/2 < k< 7/2 help (inequalities) b. Determine all values of k for which the coefficient matrix has distinct complex eigenvalues. Enter NONE if there are no values of k for which the coefficient matrix has distinct complex eigenvalues. k>7/2, k<(-7/2) help (inequalities) c. For what values of k found in part (a) does VY1(t)2 + y2(t)2 → 0 as t + 0 for every initial vector yo? Enter NONE if there are no values of k for which this is true. -sqrt(6) < k < sqrt(6) help (inequalities)
Consider initial value problem -6 k j' j, j(0) = Jo, k 1 where k is a real parameter. a. Determine all values of k for which the coefficient matrix has distinct real eigenvalues. Enter NONE if there are no values of k for which the coefficient matrix has distinct real eigenvalues. -7/2 < k< 7/2 help (inequalities) b. Determine all values of k for which the coefficient matrix has distinct complex eigenvalues. Enter NONE if there are no values of k for which the coefficient matrix has distinct complex eigenvalues. k>7/2, k<(-7/2) help (inequalities) c. For what values of k found in part (a) does VY1(t)2 + y2(t)2 → 0 as t + 0 for every initial vector yo? Enter NONE if there are no values of k for which this is true. -sqrt(6) < k < sqrt(6) help (inequalities)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:. Consider initial value problem
[
-6 k
j' =
j, 7(0) = Jo,
1
where k is a real parameter.
a. Determine all values of k for which the coefficient matrix has distinct real eigenvalues. Enter NONE if there are no values of k for
which the coefficient matrix has distinct real eigenvalues.
-7/2 < k< 7/2
help (inequalities)
b. Determine all values of k for which the coefficient matrix has distinct complex eigenvalues. Enter NONE if there are no values of
k for which the coefficient matrix has distinct complex eigenvalues.
k>7/2, k<(-7/2)
help (inequalities)
c. For what values of k found in part (a) does Vy1(t)2 + y2(t)2 → 0 as t - 0 for every initial vector yo? Enter NONE if
there are no values of k for which this is true.
-sqrt(6) < k < sqrt(6)
help (inequalities)
||
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