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Limit of an explicitly unsolvable differential equation

  1. Feb 14, 2009 #1
    1. The problem statement, all variables and given/known data
    initial value problem:

    x(0)=-6

    dx/dt=e^((x^2)/2)sin(5x)

    find the limit of x(t) as t approaches infinity.

    --I'm really unsure as to how to approach this... I was thinking along the lines of seeing where the derivative equalled zero (since if the rate of change is zero it would be indicative of a limit..) but then because of sin(5x) there are so many possibilities to this and I wasn't sure how to incorporate the initial value.

    Any help would be really appreciated!!! Thanks :)
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 14, 2009 #2

    Dick

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    Science Advisor
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    x(t) can only have a limit L if x'(L)=0. That means sin(5L)=0. Which limiting value can you possibly approach? Is it a stable point?
     
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