Right. But you're just going to use the part of
I don't get Can you post your work?
... and now, in order to clarify what I ment in my post, let's suppose that is...
... or , which is the same, ...
... where is the so called 'Heavyside Step Function'. The (2)-(3) is what I called 'head' of g(t). Now if we write (1) in term of Laplace Transform we have...
... and from (4)...
Now we can derive y(t) performing the inverse LT of (5)...
... and it is evident in (6) that the 'queue' of the y(t) when we take into account the only 'head' of g(t) doesn't vanish after . The initial problem is of course more complex because we have to consider also the 'queue' of g(t) that is...
Reply to chisigma,
I still don't understand the term 'queue'. It seems that by 'head' you mean 'the rule of association' corresponding to a function.
satisfies the DE and all initial conditions, and is also continuous. Therefore, it solves the IVP in the OP. Am I missing something here?