Consider the initial value problem x1(0) = 2, x2(0) = 6. 4x2, -4x1 + 8x2, Find the eigenvalue A, an eigenvector v1, and a generalized eigenvector v2 for the coefficient matrix of this linear system. 1 4,4 1 1 help (numbers) help (matrices) Find the most general real-valued solution to the linear system of differential equations. Use c and c2 to denote arbitrary constants, and enter them as "c1" and "c2". x1(t) cle^(4t) help (formulas) x2(t) help (formulas) Solve the original initial value problem. 1(t) 4e^(4t) help (formulas) x2(t) : 4e^(4t)+2 help (formulas)

Consider the initial value problem x1(0) = 2, x2(0) = 6. 4x2, -4x1 + 8x2, Find the eigenvalue A, an eigenvector v1, and a generalized eigenvector v2 for the coefficient matrix of this linear system. 1 4,4 1 1 help (numbers) help (matrices) Find the most general real-valued solution to the linear system of differential equations. Use c and c2 to denote arbitrary constants, and enter them as "c1" and "c2". x1(t) cle^(4t) help (formulas) x2(t) help (formulas) Solve the original initial value problem. 1(t) 4e^(4t) help (formulas) x2(t) : 4e^(4t)+2 help (formulas)

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

Consider the initial value problem
4x2,
x1(0) = 2,
-4x1 + 8x2, x2(0) = 6.
Find the eigenvalue A, an eigenvector v1, and a generalized eigenvector v2 for
the coefficient matrix of this linear system.
1
4,4
1
1
help (numbers) help (matrices)
Find the most general real-valued solution to the linear system of differential
equations. Use c and c2 to denote arbitrary constants, and enter them as "c1"
and "c2".
x1(t)
cle^(4t)
help
(formulas)
x2 (t)
help
(formulas)
Solve the original initial value problem.
x1(t) :
4e^(4t)
help
(formulas)
x2(t) :
4e^(4t)+2
help
(formulas)

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