How can one derive transfer function from initial conditions to output ?

Hello everyone!
I am looking for the needed technique for few days now and struggle to find it, hopfully I will manage to get help here.

I have a system with no input, the system is represented by matricular differential equation.
The system does not have any input, i.e. vector U=0 and therefore I dont have matrix B.
I do have Matrix A, Matrix C and I know vectors x and y variables:
dx/dt = Ax
x(t=0) = x0
y = cx

[Dimenssions: |A|=5x5 , |C|=3x5, |x| = 5X1

My question is - Is it possible to derive a transfer function (Laplace domain) from the inital conditions vector x0 to the output y ?
If so, please help me understand how, what is the technique?
If you know how to do it in MATLAB, even better!

Thanks a lot to everyone who is willing to help.