. 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.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
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Chapter2: Second-order Linear Odes
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(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.
Transcribed Image Text: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.
Transcribed Image Text: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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