ODE question, appreciate your help!

The equation of the most elementary reversible chemical reaction. Your equation is OK. Just use conservation of mass which enables you to get the equation in one dependent variable only.

I don't see the point of the 2 either*. I suggest you reframe it as A ⇔ B with the rate constants half those given.

Since this seems meant to trip students up, I suggest you placate them by using the symbols they ask, a and b.


* Unless by any chance the context suggests they mean a mechanism in which two molecules of A collide and transform into something that rapidly dissociates into two molecules of B, in which case the d.e. would be different. However if you have never done the more elementary one before then are unlikely to mean this.

 

I can't offer more than

plus my *footnote in post.

Sometimes here we have to spend too much time on exegesis, working out what a question could possibly mean. This looks like a printed text, if we saw more of where it came from, e.g. the textbook section, or the section on which it is an exercise, we'd know better what the problem is.