d 3 x 5d2x dx 17 dt2 dt3 dt 13x d u dt3 du 5 dt 6u SolutionA

d 3 x 5d2x dx 17 dt2 dt3 dt 13x d u dt3 du 5 dt 6u

Solution

Assume an initial value of 0 for all constants, take laplace of both sides
you will get,

(s³ + 5s² + 17s + 13).F(s) = (s³ + 5s + 6).U(s)

Transfer function, T(s) = F(s)/U(s)

so,

T(s) = (s³ + 5s + 6)/(s³ + 5s² + 17s + 13)