A direct derivation of the steady-state solution, when it exists, of a system ofdifferential equations can often be found by the following procedure. Assumingthat the system evolves to constant values for large times, all time derivativescan be set to zero. The problem reduces to a system that can often be solvedanalytically. Use this procedure to find the steady-state solution directly from(4.22), (4.23), and (4.24), verifying (4.28).dM,Мо — М,-dtT1(4.22)dMrwoMy(4.23)-dtT2dMyMy-woM,T2(4.24)-dtM2(0) = M,(0) = 0,M¿(∞) = Mo (4.28)

In this question, we find the steady-state solution of the differential equation by setting al the…

Answered: find the steady-state solution directly

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find the steady-state solution directly

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.5: Iterative Methods For Solving Linear Systems

Problem 23EQ

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Question

A direct derivation of the steady-state solution, when it exists, of a system of
differential equations can often be found by the following procedure. Assuming
that the system evolves to constant values for large times, all time derivatives
can be set to zero. The problem reduces to a system that can often be solved
analytically. Use this procedure to find the steady-state solution directly from
(4.22), (4.23), and (4.24), verifying (4.28).
dM,
Мо — М,
-
dt
T1
(4.22)
dMr
woMy
(4.23)
-
dt
T2
dMy
My
-woM,
T2
(4.24)
-
dt
M2(0) = M,(0) = 0,
M¿(∞) = Mo (4.28)

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