- #1
Stefania
- 11
- 0
I have trouble solving this first order nonlinear ODE :
[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!
[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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