I am trying to solve in Maple the system 
d{x}/dt =(1  1 \\1  -1).{x}
with initial conditions {x(0)} =(1 \\ -1),
where {x} is a vector.

This is what I did up to now

with(DEtools):
M1:=<1,1;1,-1>;
matrixDE(M1,t);
FM:=matrixDE(M1,t)[1];

but I am not sure how to correctly input the initial conditions to find a solution to the problem. I would appreciate any help provided.