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Asymptotic solution to a differential equation

  1. May 8, 2006 #1
    if we have the equation:

    [tex] y^{n}= F(y, \dot y, \ddot y, \dddot y,...........,y^{n-1} ) [/tex]

    where F can be a very difficult expression in the sense that can be non-linear and so on..my question is ¿how could we get an asimptotyc solution
    y(x) with x--->oo of the differential equation...thanks.
     
  2. jcsd
  3. May 8, 2006 #2
    Last edited by a moderator: Apr 22, 2017
  4. May 13, 2006 #3
    and there is no form to know how the differential equation diverges?..for example let,s suppose that for big x [tex] y(x) \sim x^{a} [/tex] where a is a real and positive exponent then my question is if there would be any way to calculate a..thank you.
     
  5. May 13, 2006 #4

    Clausius2

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    There's no general method for working out the asymptotic behavior of non linear differential equations. When it is non linear you're on your own. We usually assume a dominant balance and afterwards check it out, or we assume a behavior as you did. Your "a" can be calculated substituting your expression (if suitable) in the differential equation.
     
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