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I have a first order ODE

[tex]

yy'=a(x)+b(x)c(y)

[/tex]

and all I want to know is [itex]y'(\infty)[/itex]. Is there an easy way to find out or at least for some special forms of [itex]c(y)[/itex]?

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

[tex]

yy'=a(x)+b(x)c(y)

[/tex]

and all I want to know is [itex]y'(\infty)[/itex]. Is there an easy way to find out or at least for some special forms of [itex]c(y)[/itex]?

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

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