The general form of a linear, homogeneous, second-order equation with constant coefficients is (d^2 y/dt^2) + p(dy/dt) + qy = 0. (a) Write the first-order system for this equation, and write this system in matrix form. (b) Show that if q does not = 0, then the origin is the only equilibrium point of the system. (c) Show that if q does not = 0, then the only solution of the second-order equation with y constant is y(t) = 0 for all t.

The general form of a linear, homogeneous, second-order equation with constant coefficients is (d^2 y/dt^2) + p(dy/dt) + qy = 0. (a) Write the first-order system for this equation, and write this system in matrix form. (b) Show that if q does not = 0, then the origin is the only equilibrium point of the system. (c) Show that if q does not = 0, then the only solution of the second-order equation with y constant is y(t) = 0 for all t.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 16EQ

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