I have trouble solving this first order nonlinear ODE :(adsbygoogle = window.adsbygoogle || []).push({});

[TEX] f'(x) = \frac{af(x)[f(x)-bx]}{(1-c+bdx)f(x)+bcx-df(x)^2}[/TEX]

where [TEX]a,b,c,d\in\Re_+[/TEX] are parameters and [TEX]x\in\Re_+[/TEX].

The particular solution I am looking for should be such that:

[TEX] f'(x) &>& 0\\

\lim_{x\rightarrow 0}f(x) &=&0\\

f(x)&\geq & bx[/TEX]

Also, the solution should lie above the line [TEX]bx[/TEX] and below the following function [TEX]g(x)[/TEX]:

[TEX]g(x)=\frac{-(c-1-bdx)+ \sqrt{(c-1-bdx)^2+4bcdx}}{2d}[/TEX]

This problem is driving me nut! Any help/suggestion would be greatly appreciated!!!

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# Desperate with this ODE!

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