Let A = 0 0 1 0 0 1 -12 -19 -8 (a) Find all the eigenvalues and eigenvectors of A. (b) Suppose x, y and z are functions of t. Find the general solution of the following system of DES. x' y' = z = -12x - 19y - 8z dx dt = Y (c) By part (b), find the particular solution of the following IVP. d³x d²x +8- +19. dt³ dt² + 12x = 0, x(0) = 1, x'(0) = 1, x'(0) = 1, x" (0) = 1.
Let A = 0 0 1 0 0 1 -12 -19 -8 (a) Find all the eigenvalues and eigenvectors of A. (b) Suppose x, y and z are functions of t. Find the general solution of the following system of DES. x' y' = z = -12x - 19y - 8z dx dt = Y (c) By part (b), find the particular solution of the following IVP. d³x d²x +8- +19. dt³ dt² + 12x = 0, x(0) = 1, x'(0) = 1, x'(0) = 1, x" (0) = 1.
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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Question
![2.
0 1 0
-89
0 0 1
-12 -19 -8]
Let A =
(a) Find all the eigenvalues and eigenvectors of A.
(b) Suppose x, y and z are functions of t. Find the general solution of the following
system of DES.
x' =
1
y'
=
y
2
-12x 19y - 8z
(c) By part (b), find the particular solution of the following IVP.
d³x d²x
+8. +19-
dt³ dt²
dx
+ 12x = 0, x(0) = 1,
x(0) = 1, x'(0) = 1, x"(0) = 1.
dt](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff270a057-74c3-4dcb-bc49-7083cb266e44%2Fd77e2d11-67ab-4e8c-954f-6867164ddd24%2Fblfdrsr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2.
0 1 0
-89
0 0 1
-12 -19 -8]
Let A =
(a) Find all the eigenvalues and eigenvectors of A.
(b) Suppose x, y and z are functions of t. Find the general solution of the following
system of DES.
x' =
1
y'
=
y
2
-12x 19y - 8z
(c) By part (b), find the particular solution of the following IVP.
d³x d²x
+8. +19-
dt³ dt²
dx
+ 12x = 0, x(0) = 1,
x(0) = 1, x'(0) = 1, x"(0) = 1.
dt
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