Consider the initial value problem:4x2,x1(0) = -1,x2(0) = 1.-4x1 + 8x2,a. Find the eigenvalue A, an eigenvector v, and a generalized eigenvector w for the coefficient matrix of this linearsystem.1=4.V =W =1b. Find the most general real-valued solution to the linear system of differential equations. Use c1 and c2 to denotearbitrary constants, and enter them as "c1" and "c2".x1(t) =x2(t) =%3D =1V =0.W =1b. Find the most general real-valued solution to the linear system of differential equations. Use c andarbitrary constants, and enter them as "c1" and "c2".C2 to denoteC1¤1(t)x2(t)c. Solve the original initial value problem.1x1(t) =4xetx(V10 sin(4V 10 x) + 5 cos(4V10 x))x2(t) =

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Consider the initial value problem: 4x2, a1(0) = -1, -4x1 + 8x2, 2(0) = 1. a. Find the eigenvalue X, an eigenvector v, and a generalized eigenvector w for the coefficient matrix of this linear system. 1 0. 4. w = 1 b. 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". a1(t)

Consider the initial value problem: 4x2, a1(0) = -1, -4x1 + 8x2, 2(0) = 1. a. Find the eigenvalue X, an eigenvector v, and a generalized eigenvector w for the coefficient matrix of this linear system. 1 0. 4. w = 1 b. 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". a1(t)

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) = -1,
x2(0) = 1.
-4x1 + 8x2,
a. Find the eigenvalue A, an eigenvector v, and a generalized eigenvector w for the coefficient matrix of this linear
system.
1
=
4.
V =
W =
1
b. Find the most general real-valued solution to the linear system of differential equations. Use c1 and c2 to denote
arbitrary constants, and enter them as "c1" and "c2".
x1(t) =
x2(t) =
%3D

=
1
V =
0.
W =
1
b. Find the most general real-valued solution to the linear system of differential equations. Use c and
arbitrary constants, and enter them as "c1" and "c2".
C2 to denote
C1
¤1(t)
x2(t)
c. Solve the original initial value problem.
1
x1(t) =
4x
etx(V10 sin(4V 10 x) + 5 cos(4V10 x))
x2(t) =

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