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An approximation of a differential equation

  1. Sep 21, 2007 #1


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    1. The problem statement, all variables and given/known data
    Find an approximate oscillating soution of y'' = (y-x)^2 - exp(2*(y-x))

    where y=y(x), y'' denotes second deriviate

    2. Relevant equations
    y'' = (y-x)^2 - exp(2*(y-x))

    3. The attempt at a solution
    I try to change a variable with p = y-x, so
    dy/dx = dp/dx+1
    y'' = p''

    The original equation becomes p'' = p^2 - exp(2p)
    when p^2 close to exp(2p) or p close to exp(p), we have p'' -> 0, i.e. p -> ax+b

    I think the approximate solution is p = ax + b, but it turns out to be not. Does anyone give me some hint to find out the approximate oscillating solution? Thanks in advance
  2. jcsd
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