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Question

Two right sided signals are related through differential equations dx(t)dt=2y(t)+δ(t) and dy(t)dt=2x(t)then the initial value signal x(t) is ____

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Solution

The correct option is A 1
Taking Laplace transform of both sides of the two differential equations

sX(s)=2Y(s)+1

and sY(s)=2X(s)

sX(s)=22X(s)s+1

X(s)=ss2+4

from intial value theorem,

x(0)=limssX(s)

=limss2s2+4=1

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