# Question: A system is described by the following differential equation: d3y/dt – Free Chegg Question Answer

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## Expert Chegg Question Answer:

Answer:

## Answer

y <-> Y(s)

x <-> X(s)

dy/dt <-> sY(s)

d2y/dt2 <-> s^2.Y(s)

d3y/dt3 <-> s^3 Y(s)

Substitute:

s^3.Y(s) + 3s^2.Y(s) + 5sY(s)+Y(s) = s^3.X(s) + 4s^2.X(s) + 6s.X(s) + 8X(s)

H(s) = Y(s)/X(s) = (s^3 + 4s^2 + 6s +8)/(s^3 + 3s^2 + 5s +1)