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Problem with EDO and solution y=x^a

  1. Sep 16, 2006 #1
    Let's suppose we have a linear (or non linear) EDO:

    [tex] F(x,y,y',y'',y''',....)=0 [/tex] we don't know how to solve it..:frown: but we know that the EDO has a "particular" solution [tex] y_{0} (x)=x^{a} [/tex] where a can be a real or complex number.. then if we apply the operator:

    [tex] D^{a+1}y_{0} (x) =0 [/tex] (fractional differential operator)

    Unfortunately we don't know what "a" is my main question is ┬┐could it be calculated exactly?..thanks. (i'm refering to the exponent a ) :grumpy: :grumpy:
  2. jcsd
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