Nonlinear DE similar to a Bernoulli equation

[bradbrad]

Hi all,

I've got a nonlinear differential equation of the general form

y' + f(x)y + g(x) = h(x)(y^n)

to solve.

For g(x) = 0 this is your standard Bernoulli equation. I've been trying to think of a way to solve it but haven't managed so far.

Any ideas would be appreciated.

Many thanks.

Brad.

 

[bigfooted]

This equation is called Chini's equation. There is no general solution method known. However, for specific choices of the unknown functions you can find a solution, e.g. by searching for symmetries (e.g. kolokolnikov and cheb-terrab - assume it has linear symmetries). This is equivalent to the original solution algorithm of Chini.

 

[bradbrad]

Many thanks for that bigfooted.

I think I'm just going to linearise it.