Circuits II Laplace and differential equation question

Question

Find the

differential equation

relating

()Find the

find a differential equation relating c(t) and r(t) if:

C(s)/R(s) = (s + 1)/(s(s+2)(s+3))

ct

and

()

rt

if

Answer 1

C(s)(s(s+2)(s+3) = R(s)(s+1) C(s)(s(s² +5s +6)) = R(s)s +R(s) so now C(s)s³ +C(s)5s² +C(s)6s = R(s)s +R(s). So the differential equation would become d³c(t)/dt³ + 5d²c(t)/dt² +6dc(t)/dt =dr(t)/dt +r(t) all initial conditions are considered to be 0. Hence c'''(t) + 5c''(t) + 6c'(t) =r'(t) + r(t).