Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Linearization of nonlinear non homogenous ODE

  1. Jun 23, 2008 #1
    Hi everybody,
    could anyone help me in the linearization of the following non linear non-homogeneous ODE?


    where A, B and C are constants. y is a function of t. is it possible to reduce this equation to a Riccati equation? do you know any analytical, approximate or not, methods to solve the equation?

    thanks in advance
  2. jcsd
  3. Jun 23, 2008 #2


    User Avatar
    Homework Helper

    Just to be clear, is this the DE:

    [tex]A \frac{dy}{dt} + By^4 = C[/tex]

    If so, then note that you can easily express it as a http://en.wikipedia.org/wiki/Bernoulli_differential_equation" [Broken]and solve it directly without having to approximate it.
    Last edited by a moderator: May 3, 2017
  4. Jun 27, 2008 #3
    the DE is right...the BERNOULLI equation is homogeneous and I actually can't tarnsform my equation in a Bernoulli one. can you suggest me how to transform it?
  5. Jun 27, 2008 #4


    User Avatar
    Homework Helper

    I just had a second look at the DE and realised that there is no need to solve it as a Bernoulli DE. The original DE is separable, though the resulting integral is a little tough to integrate, but certainly doable.
  6. Jul 2, 2008 #5
    i have found in literature the Chini equation, which is similar to the equation I'm trying to solve. unfortunately i can't found the solution. can everyone help me, please?
  7. Jul 2, 2008 #6


    User Avatar
    Science Advisor

    Defennder has already pointed out that this equation is separable:
    [tex]/frac{Ady}{C- By^4}= dt[/tex]
    Integrate both sides, using "partial fractions" on the left.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook