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A Nonhomogeneous second order nonlinear differential equations

  1. Apr 11, 2016 #1
    • Member warned about posting a question so scant on details
    Hello every one,
    I have an equation related to my research. I wonder if any one has any suggestion about solving it?
    y''+y' f(y)+g(y)=h(x)

    thanks
     
  2. jcsd
  3. Apr 11, 2016 #2
  4. Apr 12, 2016 #3
  5. Apr 12, 2016 #4
    Can you give us more details about your equation. What you have written is a very general 2nd order nonlinear equation. The solution (if one exists) strongly depends on the form of f(y), g(y), and h(x). There are numerous analytical and numerical techniques that can help you find an exact or approximate solution. However, some techniques will work better than others, and the choice of which techniques to try strongly depends of f, g, and h.

    Also is your equation really the nonlinear equation [itex] y'' + y' f\left(y\right) + g\left(y\right) = h\left(x\right)[/itex] where f and g both depend on y, or is it a linear equation of the form [itex] y'' + y' f\left(x\right) + g\left(x\right) = h\left(x\right)[/itex] where f and g depend on x?
     
  6. May 14, 2016 #5
    there is no sense to speak "nonhomogeneous" about a nonlinear equation. Generally, such a type equation is not integrated explicitly. So it remains qualitative analysis or numerical analysis depending on what exactly you need from this equation
     
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