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Non-linear first order ODE

  1. Jul 23, 2011 #1
    I'm trying to solve the following ODE: [tex] ydx+(\frac {e^x}{y}-1)dy=0[/tex]

    I tried to transfer this ODE into exact form but no luck.

    Will appreciate any help.
     
  2. jcsd
  3. Jul 23, 2011 #2

    LCKurtz

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    Leave the equation as it is and look for an integrating factor that is just a function of x.
     
  4. Jul 23, 2011 #3
    I tried it before:
    [tex]X=y, Y=e^x/y-1[/tex]
    [tex]u'(x)+(\frac {X_y-Y_x}{Y})u(x)=0[/tex]
    Thus u=e^x

    But [tex]d/dy(e^xX) \neq d/dx(e^xY)[/tex]

    What I'm missing?
     
  5. Jul 23, 2011 #4

    LCKurtz

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    Are you sure about the sign on that numerator?
     
  6. Jul 23, 2011 #5
    Bellow is formula that I found in my book:
    [tex]u'(x)+(\frac {X_y-Y_x}{Y})u(x)=0[/tex]=
    [tex]u'(x)-u(x)=0[/tex] => u=e^x

    Can't see where is the problem.
     
  7. Jul 23, 2011 #6

    LCKurtz

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    I told you what was wrong. The numerator should be Yx-Xy.
     
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