Answering to StatusX: I followed your suggestion, but the equation does not get easier even factoring out the asymptotic behavior.
Everything seems to suggest that there is no exact solution to this equation.
Does anybody have a suggestion on how I could approximate the solution?
Thank you desA. I tried with numerical methods, but the problem that I have with shooting is that at the initial condition \lim_{x\rightarrow 0}f(x)=0, the function is ill-defined.
How do I scope the behaviour of my function? I believe numerical methods allow me to use the conditions I know...
sorry, I am a little slow on this...
I agree g(x) is asymptotic to bx, then how can the product bx*g(x) be also asymptotic to b(x)?
Also, I do not understand your suggestion completely: you suggest to use f'(x) and the equality f(x)=bx g(x) to derive a DE for g. Ok, but how does that make me...
Sorry, I do not understand your answer. Yes, g(x) comes from that quadratic expression, but not f. I do not understand what your answer is telling me about f...
And yes: dx is actually d*x (here d is a parameter, like a,b,c)
I know their values. I need an (approximated?) solution to the f(x) function in terms of the a,b,c,d coefficients. My ultimate goal is to study how f vary when I let the coefficients vary, and this is why I need a solution also in terms of the coefficients.
Well, little story of the equation.
I am a PhD student in Economics, I am writing a model of multinational production and international trade. That equation is a pricing rule that comes from my model.
Actually, your transformed equation is the one that I get straight from the model, and I got...
The parameters are all non-zero and positive, so the above does not solve my problem:frown:
I am happy with an approximated solution as well (power series type), I just don't manage to compute it!
Ok I try again, but it really looks that it does not work. Anyways: the problem is the following:
f'(x)=\frac{af(x)[f(x)-bx]}{(1-c+bdx)f(x)+bcx-df(x)^2}
where a,b,c,d\in\Re_+ and x\in\Re_+.
I look for a solution such that:
f'(x) > 0;\lim_{x\rightarrow 0}f(x) =0;f(x)\geq bx
The...
I have trouble solving this first order nonlinear ODE :
f'(x) = \frac{af(x)[f(x)-bx]}{(1-c+bdx)f(x)+bcx-df(x)^2}
where a,b,c,d\in\Re_+ are parameters and x\in\Re_+.
The particular solution I am looking for should be such that:
f'(x) &>& 0\\
\lim_{x\rightarrow 0}f(x) &=&0\\
f(x)&\geq & bx...