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Nonlinear DE similar to a Bernoulli equation

  1. Sep 4, 2012 #1
    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.

  2. jcsd
  3. Sep 4, 2012 #2
    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.
  4. Sep 8, 2012 #3
    Many thanks for that bigfooted.

    I think I'm just going to linearise it.
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