Actually it doesn't matter, turns out this is just following on from another example!!
First time solving DEs this way so bare with me.
Consider with and .
Using the Laplace Transform of both sides we get:
Isolating and using the initial conditions, we get:
Now in the answers I've got it says let and they then proceed to do the Laplace Transform of that and substitute it in.
Just wondering why they've chosen , is this something I've missed?