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How to estimate the behavior of a solution of a differential equation at \infty?

  1. Mar 24, 2010 #1
    i have a first order nonlinear differential equation


    the boundary condition is y(x=0)=0

    here k is a real positive number

    i want to estimate the behavior of y as x goes to infinity

    how to do this?

    any book for reference?
  2. jcsd
  3. Mar 25, 2010 #2
    As sin^2(kx+y) is bounded , sin^2(kx+y)/kx -> 0 as x->infinity. Therefore, y will tend to a constant as x->infinity , regardless of the initial condition .
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