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
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).