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Did I solve this diff eq substition problem properly?

  1. Feb 17, 2013 #1
    [itex]xy'=yln(xy)[/itex]
    [itex]xdy=yln(xy)dx[/itex]
    [itex]\frac{dy}{y}[/itex]=[itex]\frac{ln(xy)dx}{x}[/itex]

    Substitution:

    [itex]v=ln(xy)[/itex]
    [itex]dv[/itex] = [itex]\frac{dy}{y}[/itex]-[itex]\frac{dx}{x}[/itex]
    [itex]dv[/itex]-[itex]\frac{dx}{x}[/itex]=[itex]\frac{vdx}{x}[/itex]

    ∫[itex]\frac{dv}{v+1}[/itex]=∫[itex]\frac{dx}{x}[/itex]

    [itex]ln(v+1)=ln x + C[/itex]

    v+1 = Cx
    ln(xy) +1 = Cx

    Would that basically be the complete answer?
     
  2. jcsd
  3. Feb 17, 2013 #2

    mfb

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    2016 Award

    Staff: Mentor

    It might be interesting to solve this last equation for y=... and verify the answer with the initial equation.
     
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