9.13 (Solutions corresponding to poles and zeros) Consider the differential equation dy d-lu d-ly din-1 den dt-1 (a) Let A be a root of the characteristic equation + a1 ! + ... + any=b₁² d21 dtn-2 + b₂. ++bnu. s+as++an=0. Show that if u(t)=0, the differential equation has the solution y(t) = et (b) Let k be a zero of the polynomial b(s) bis + b₂8-2+... +b Show that if the input is u(t)= et, then, there is a solution to the differential equation that is identically zero.
9.13 (Solutions corresponding to poles and zeros) Consider the differential equation dy d-lu d-ly din-1 den dt-1 (a) Let A be a root of the characteristic equation + a1 ! + ... + any=b₁² d21 dtn-2 + b₂. ++bnu. s+as++an=0. Show that if u(t)=0, the differential equation has the solution y(t) = et (b) Let k be a zero of the polynomial b(s) bis + b₂8-2+... +b Show that if the input is u(t)= et, then, there is a solution to the differential equation that is identically zero.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:9.13 (Solutions corresponding to poles and zeros) Consider the differential equation
dy
d-lu
d-ly
din-1
den
dt-1
(a) Let A be a root of the characteristic equation
+ a1
! + ... + any=b₁²
d21
dtn-2
+ b₂.
++bnu.
s+as++an=0.
Show that if u(t)=0, the differential equation has the solution y(t) = et
(b) Let k be a zero of the polynomial
b(s) bis + b₂8-2+... +b
Show that if the input is u(t)= et, then, there is a solution to the differential
equation that is identically zero.
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