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Stuck on exact ODE problem.

  1. Mar 2, 2012 #1
    I'm not sure where I'm going wrong on this one so I hoped that I could find some help

    we begin with
    [itex](x^2 + y^2 + 5) dx - (y+xy) dy[/itex]

    taking both partial derivitives I found that

    [itex]2y (dy) =/ -y(dx)[/itex]

    Next I went to find my factor of integration using [itex] e^(My - Nx / N) dx)[/itex]


    This got me [itex]((1+x)^-3)[/itex]

    which i then simplified to [itex](1 + 1/x^3)[/itex]


    Then i multiplied our I.F. through the original M and N, but the problem still did not come out to be equal

    our new partial derivitives of m and n are:

    [itex]((2y/x^3)(dy) =/ ((3y/x^4) + (2y/x^3) - (y))(dx))[/itex]


    Sorry I couldn't figure out how to display notequal with itex.. anyways thanks in advance for any help
     
  2. jcsd
  3. Mar 5, 2012 #2

    HallsofIvy

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    Well, that's a problem! [itex](1+x)^{-3}[/itex] is NOT equal to
    [tex]1+ \frac{1}{x^3}[/tex]
    It is, rather,
    [tex]\frac{1}{(1+ x)^3}[/tex]


     
  4. Mar 6, 2012 #3
  5. Mar 6, 2012 #4

    HallsofIvy

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    What do you think "distribute" means there?
     
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