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.