A sixth order backward differentiation formula (BDF) need six (five plus initial value) previous solutions to get started. How I can get these previous solutions? I need a method accurate to sixth order capable of handling stiff problems.
Initializing implicit linear multistep methods
ode;implicit methods
The standard approach is to use a self-starting time-marching algorithm with sufficiently small timestep (such that the order of accuracy is not spoiled) and compute the 5 non-initial value previous solutions.  These are then used to start the BDF formula.