Ei = Et + Er
⟹ Et = Er
⟹ Et = Ei.
(s3 + 2s2 + 5s + 6)y(s) = (s2 + 4) x (s)
s3y(s) + 2s2y(s) + 5sy(s) + 6y(s) = s2 x (s) + 4 x (s)
Replacing s by and y(s) by y(t) and x(s) by x(t) we get
y(t) + 2
y(t) + 5
y(t) + 6y(t)
= x(t) + 4x(t)
+ 2
+ 5
+ 6 =
+ 4x
This is required differential equation.
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