How to make statistics on a formula

1. matteo86bo

60
Hi everyone,
I've derived a formula which computes a certain quantity. This is the equation:

$$f(x,t)=a(x,t)-\frac{1}{n}b(x)f(x,t)^{(1-n)/n}\frac{\partial f(x,t)}{\partial t}$$

I need to prove that $$f(x,t)\sim a(x,t)$$.

All I have is that $$0.5 < n < 2$$, $$b(x)$$ is a decreasing function of x (almost exponential) and $$f(x,t) = 1 +(c(x)-1)t$$ where $$c(x)$$ is another decreasing function of x.

I tried several things but I do not want to bias you answers.