Quote by arildno
We might tidy up your problem as follows:
Set [tex]\epsilon^{2}=\frac{A}{4mg},w(t)=\epsilon{v}(t)[/tex]
Multiplying your diff.eq with [itex]\epsilon[/itex], we get:
[tex]\frac{dw}{dt}=\epsilon{g}(1w^{2})[/tex]
Agreed so far?

Took quite some time to mentally process(This format is extremely unfamiliar) and sure. I'm not really sure where you go from here(My experience with differential equations is practically nothing, beyond several glimpses on wikipedia.) but I guess I can shoot off into several random directions and hope one hits the target.