Dear friends,

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 thefundamental solutionis 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).

Thanks.