I'm developing a simple simulation environment for compartmental models and want to use the exponential euler as numerical integration method.
My main problem is that: exponential Euler assumes an equation in the form of

however, I just can't work out, how the equation

could fit into that pattern.
All literature I found jump from the first equation directly to the second (or the other way around) but they don't explain of which values A and B consist of.
I hope someone can help me with that problem since I really want to understand what I'm doing.
Regards