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First Order DE

  1. May 9, 2012 #1
    Hello

    Comming from Discrete Mathematics, I have very little knowledge in Solving ODEs:

    I have the following equation (where E(x) is an ordinary generating function).

    [itex]E'(x) = \frac{(E(x)*E(x) +E(x)-x)}{2x*E(x)}[/itex]

    with E(0) = 0
    Is there any hope to solve this equation?
     
    Last edited: May 9, 2012
  2. jcsd
  3. May 9, 2012 #2

    mathwonk

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    there is always hope. have you looked at picard's method? what do you mean by "solve"? the usual procedure is to give a sequence of approximations that converge to a solution.
     
  4. May 10, 2012 #3
    Hello !
    The analytical solution involves the special function erfi.
    The solution is expressed on a parametric form (see attachment).

    The part previously entitled "Formal solution" has been deleted. There was a mistake in it.
     

    Attached Files:

    Last edited: May 10, 2012
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