Here are two technical recommendations on how to apply Hint 3:
To express \frac{\mathrm d a}{\mathrm dt} and \frac{\mathrm d b}{\mathrm dt} in terms of a and b, it is convenient to first express these rates of change in terms of the half-angle \alpha between two neighbouring bird velocities, and then express this angle in terms of a and b.
To solve the differential equation relating \frac{\mathrm d a}{\mathrm db} to a and b, one can denote a/b=x (or b/a=x), and solve the obtained differential equation relating \mathrm da and \mathrm dx to a and x (or \mathrm db and \mathrm dx to b and x).
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