If the system T.F. is The differential equation representing the system is

(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) + 2y(t) + 5y(t) + 6y(t)

= x(t) + 4x(t)

+ 2 + 5 + 6 = + 4x

This is required differential equation.