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dp/dt = A*f(r)

dr/dt = -B*h(r)

where A and B are constants greater than zero. I'm trying to find linear functions that will tend to equillibrium, and also where

limit df(r)/dt = 0

r->0

I have been trying various linear functions and have been unable to come up with a solution. Is there a solution? and if so, what would be one? It's probalby something simple that I'm overlooking. Any help would be appreciated. Thanks.