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Homework Help: The Devil's in the Algebra.

  1. Feb 22, 2004 #1
    I need to put this general solution to a differential in the following form:

    My solution is in the form (-x^3)(y^(-1)) + (x^2)y = C

    It needs to be in the form y = (x^(-2))[c+-((c^2) + x^5)^(1/2)]

    I've been noodling around with it for a while and it's not working out for me. Does anyone something I can factor out or multiply by that will put it into a friendlier form?

    Thanks.
     
  2. jcsd
  3. Feb 22, 2004 #2

    NateTG

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    Homework Helper

    You've got:
    [tex]\frac{-x^3}{y}+x^2y=C[/tex]
    [tex]-x^3=Cy-x^2y^2[/tex]
    Which is a quadratic equation in [tex]y[/tex].
    [tex]x^2y^2-Cy-x^3=0[/tex]
    Apply the quadratic formula, and you should get there.
     
  4. Feb 22, 2004 #3
    Multiply through by y and you have a quadratic equation in the y variable.

    cookiemonster
     
  5. Feb 23, 2004 #4
    Thanks.

    I should have seen this. It's a no brainer. Where was my brain last night?[zz)]
     
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