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Differential Equation, Separable, I believe

  1. May 13, 2010 #1
    Haven't done one of these in awhile and I was looking for a place to make sure I was doing it right. Hopefully one of you can take the time to look it over?

    1. The problem statement, all variables and given/known data

    Find the unique solution of the differential equation (3y^2)x(dy/dx)-x+1=0 for which y(e)=1

    2. Relevant equations

    None.

    3. The attempt at a solution

    (3y^2)dy=((x-1)/x)dx

    Integrate

    y^3=x-lnx+C

    Substitute in for unique solution

    1^3=e-ln(e)+C
    2-e=C
     
  2. jcsd
  3. May 13, 2010 #2

    tiny-tim

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    Welcome to PF!

    Hi Marylander ! Welcome to PF! :smile:

    (try using the X2 tag just above the Reply box :wink:)
    Looks good! :biggrin:
     
  4. May 13, 2010 #3
    Didn't think to. Too used to not having it.

    Good, thanks for checking.
     
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