A system of coupled ODEs, where x = x(t), are expressed in the matrix form = 7 x' = (-1034)x where x = (x) with initial values x(0) = (-3). i. ii. iii. iv. V. State the two 1st order ODES. Find the eigenvalues and eigenvectors analytically. Using Matlab, show that your solutions to ii are correct (include screenshot). Find the particular solutions to x(t) and y(t). What are the values of x(t) and y(t), to 3 s.f., when t=5?

A system of coupled ODEs, where x = x(t), are expressed in the matrix form = 7 x' = (-1034)x where x = (x) with initial values x(0) = (-3). i. ii. iii. iv. V. State the two 1st order ODES. Find the eigenvalues and eigenvectors analytically. Using Matlab, show that your solutions to ii are correct (include screenshot). Find the particular solutions to x(t) and y(t). What are the values of x(t) and y(t), to 3 s.f., when t=5?

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

A system of coupled ODEs, where x = x(t), are expressed in the matrix form
x' = (-1034)x where x = (
= (³)
with initial values x(0) = (-3).
i.
ii.
iii.
iv.
V.
State the two 1st order ODES.
Find the eigenvalues and eigenvectors analytically.
Using Matlab, show that your solutions to ii are correct (include screenshot).
Find the particular solutions to x(t) and y(t).
What are the values of x(t) and y(t), to 3 s.f., when t=5?

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