I have a problem with the solution representation formula for first-order (delay) differential equations.
Let , and be a function such that for all and .
Let , and .
Consider the following differential equation:
Then, can be represented in the following form uniquely:
for , where are assumed to be identically zero out of their domains, and the fundamental solution is the solution of the following differential equation:
In (3), are same as in (1).
I would be glad if some one can help me with the proof of the representation formula (2).