Thanks for your fast response.

I'm still not quite sure how I am going to set it up. I have found the piece of paper with my supervisors hints. He does this:

(which is what you said basically)

and sets up x' = Ax, which has solution

This is the analytical solution and I understand it, but I'm kind of confused on the numerical methods way of doing it.

I think its meant to be RK4 on

and then on

, but what do I do with these two outputs?

I'm fairly sure the original equation is only meant to have 1 output.