ystems(b) Show that if q #0, then the origin is the only equilibrium point of the system.(c) Show that if q #0, then the only solution of the second-order equation with yconstant is y(t) = 0 for all t. 16. The general form of a linear, homogeneous, second-order equation with constantcoefficients isd² y dy+ pdt² dt+qy = 0.(a) Write the first-order system for this equation, and write this system in matrixform.

. The general form of a linear, homogeneous, second-order equation with constant coefficients is d²y dy + p dt2 dt + qy = 0. (a) Write the first-order system for this equation, and write this system in matrix form.

. The general form of a linear, homogeneous, second-order equation with constant coefficients is d²y dy + p dt2 dt + qy = 0. (a) Write the first-order system for this equation, and write this system in matrix form.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter1: Systems Of Linear Equations

Section1.1: Introduction To Systems Of Linear Equations

Problem 90E: Consider the system of linear equations in x and y. ax+by=ecx+dy=f Under what conditions will the...

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Question

ystems
(b) Show that if q #0, then the origin is the only equilibrium point of the system.
(c) Show that if q #0, then the only solution of the second-order equation with y
constant is y(t) = 0 for all t.

16. The general form of a linear, homogeneous, second-order equation with constant
coefficients is
d² y dy
+ p
dt² dt
+qy = 0.
(a) Write the first-order system for this equation, and write this system in matrix
form.

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