Does anybody suggest how to face the inhomogeneous Bernoulli differential equation $y'+P(x)y=Q(x)y^n+f(x)$ for the simple case $f=const.$ and for the generic case. I would like to know about techniques of approximation, bounds, asymptotic limit, numerical techniques etc. Thank you Roberto

I presume your $f(t)$ should be $f(x)$. This is Chini's equation. See e.g. http://www.maplesoft.com/support/help/Maple/view.aspx?path=odeadvisor/Chini 


Solution: let u=y^(1n) du/dx = (1n) y^(n) dy/dx = (1n) y^(n) [ Py+Qy^n+f] =(1n) Pu +(1n)Q +(1n)f u^(n/n1) Separation of variables [1/(1n)]Int[du/ { f u^(n/n1)+PuQ}]= Int[dx]= x+ C Factor out the division and integrates the LHS. We get F(u,x)=0 then transform into F(y,x)=0. For n=2, it is very easy to solve. You can try it. 

