> v*x + y*dx/dt - x*dy/dt = 0
>
> It's been a while since I've done any differential equations, so I didn't 
> go this route.  Instead I eliminated the `t' variable and rewrote 
> everything in terms of just the position of the boat (i.e. x and y).  In 
> this view you get the differential equation:
>
> dy/dx = y/x - v*sqrt(1+(y/x)^2)

That would have been the step I couldn't figure out - it's been a while 
since I did this type of thing regularly!

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