you can change to the "scaled variables" Y= y/(a/b) and X= x/(m/n) by solving those for x and y: x= (m/n)X and y= (a/b)Y. Then the differential equations become

or

and

or

which have equilibrium points at (0, 0) and (1, 1).

You then get

which can be separated as

Integrate that to get g(Y)= f(X).