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DE Auxilary Equation

  1. Oct 16, 2011 #1
    I need to find a solution to:
    [tex]x^{2}y"-xy'+y=0[/tex] in the form of [tex]y=x^{r}[/tex] where r is a constant.

    I started by finding the appropriate derivatives:

    Then substituting in:
    which simplifies to:

    I then solved and got the complex roots:
    [tex]\frac{1\pm i\sqrt{3}}{2}[/tex]

    I'm not sure what to do next. The examples I've seen so far have separated out the imaginary part using identities, where the function is exponential.
  2. jcsd
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