Final answer:
To find the differential equation from the given transfer function with delay terms, one must apply inverse Laplace transforms, with possible need for complex algebraic manipulation. The delays in the system are indicated by exponentials with 5 and 2 seconds delay times.
Step-by-step explanation:
To convert the given transfer function H(s) = Y(s)/U(s) = (e−5+0.7)/(s2+2e−2s+2)4 into a corresponding differential equation, you must take the inverse Laplace transform and express Y(s) and U(s) as functions of time. In this transfer function, we can identify the presence of delay terms indicated by the exponential elements such as e−5 and e−2s. The delay times for these terms can be determined by the exponent of the e.
However, due to the complexity of this function, specifically the raised power in the denominator, converting it to the time domain is not straightforward and may require decompositions or advanced methods such as using a computer algebra system to obtain the explicit form of the differential equation. The delayed terms e−5 and e−2s suggest the presence of delayed responses in the system with time delays of 5 and 2 seconds, respectively.