A causal LT1 system with impulse response h(t) has the following properties: 1. When t...

A causal LT1 system with impulse response h(t) has the following properties:

1. When the input to the system is for all t, the output is for all t.

2. The impulse response h(t) satisfies the differential equation

where b is an unknown constant.

Determine the system function H(s) of the system, consistent with the information above. There should be no unknown constants in your answer, that is, the constant b should not appear in the answer.