Your way of writing this is awkward but I think you mean
However, since the ' indicates the derivative and there is no "t+1" or other time change, this is NOT a "difference equation" so perhaps that is not what you mean. Assuming is a given function, we can rewrite this as .
Without knowing both and the best we can do is write the solution to that equation as so that .
You should be able to answer your questions from that.