Asymptotic behaviour of 1st order ODE

[Gerenuk]

I have a first order ODE
<br /> yy&#039;=a(x)+b(x)c(y)<br />
and all I want to know is y&#039;(\infty). Is there an easy way to find out or at least for some special forms of c(y)?

Eventually I'd like to find functions a, b, c such that there is a solution with (x=\infty,y=-V) (x=\infty,y=V\alpha) for any V where \alpha is a given factor. Preferably with a(x)=-Ax^{-n}

 

[MathematicalPhysicist]

If you know that y(\infty)=-V, so you know that y&#039;(\infty)=[a(\infty)+b(\infty)c(-V)]/(-V), you must know beforehand what are b,c,a are to find it.

 

[Gerenuk]

I can chose a, b, c as given. And V is basically whatever y' is in one solution.
The important point is that the other y' solution at infinity should be a given factor \alpha of the first solution.
Maybe I should say where the problem came from. I basically want to find a physical law such that an object bouncing off a wall will lose a given part 1-\alpha of its velocity. So I have the wall force a and the damping force b which should both be concentrated at the wall only.
And yy&#039; is the force on the particle after a mathematical transformation.

Oh I just notice I might have mixed up the variables after the transformation...
I want to know (x,y) as given with the points. I don't need y'.