Control systems -- input with non-zero initial conditions

[mattyboson12]

Homework Statement

Deriving an s-domain equation for the following inputs a) &b)

The Attempt at a Solution

I understand how to derive the equation for an input with zero initial conditions (part a) but I'm not sure what to do when there are non-zero initial conditions (part b)

 

[Filip Larsen]

Which Laplace transformation rules do you think may be relevant here? Specifically, is there any way you can retrieve the system function from R in a)? And in b), perhaps you can express the input as a sum of something?