3+13 -t 5. Consider the vector valued functions x₁(t)= and x₂(t)= t2 -(3) (a)Compute the Wronskian W[x₁,x₂](t). (b) Find a matrix valued function A(t) such that X₁, X₂ form a dx dt dx. dt fundamental set of solutions to the system Wronskian W[x₁,x₂](t)=0. (c) Give a general solution to the system =A(t)x with the A(t) found - A(t)x whenever the -2 (e)Solve the initial value problem with X(1)= T above. (d) Find the natural fundamental matrix associated with the initial time t₁ =1 for this system.
3+13 -t 5. Consider the vector valued functions x₁(t)= and x₂(t)= t2 -(3) (a)Compute the Wronskian W[x₁,x₂](t). (b) Find a matrix valued function A(t) such that X₁, X₂ form a dx dt dx. dt fundamental set of solutions to the system Wronskian W[x₁,x₂](t)=0. (c) Give a general solution to the system =A(t)x with the A(t) found - A(t)x whenever the -2 (e)Solve the initial value problem with X(1)= T above. (d) Find the natural fundamental matrix associated with the initial time t₁ =1 for this system.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
.
(b) Find a matrix valued function A(t)such that X₁
dx
dt
and X₂(
₂(t)=
=
$2
dx.
fundamental set of solutions to the system =
dt
Wronskian W[x₁,x₂](t)#0.
(c) Give a general solution to the system
above.
(d) Find the natural fundamental matrix associated with the initial time
t₁ =1 for this system.
-2
(e)Solve the initial value problem with X(1)= T
form a
t2
A(t)x whenever the
A(t)x with the A(t) found](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8aa10308-c186-4690-945e-554747bf90d8%2Fc34d9c56-b288-4b17-be8e-fdcb69cb08d4%2Fwhq4snf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3+13
5. Consider the vector valued functions X₁ (t)=
(a)Compute the Wronskian W[x₁,x₂](t).
(b) Find a matrix valued function A(t)such that X₁
dx
dt
and X₂(
₂(t)=
=
$2
dx.
fundamental set of solutions to the system =
dt
Wronskian W[x₁,x₂](t)#0.
(c) Give a general solution to the system
above.
(d) Find the natural fundamental matrix associated with the initial time
t₁ =1 for this system.
-2
(e)Solve the initial value problem with X(1)= T
form a
t2
A(t)x whenever the
A(t)x with the A(t) found
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