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Homework Help: Help with differential equation

  1. Feb 26, 2010 #1
    Hello :)

    I'm trying to solve an homogeneous equation... but it seems that i'm wrong in some step... or something, because I can't complete this problem, look here is what i got:

    1. The problem statement, all variables and given/known data
    Solve the given homogeneous equation:
    [tex]x\frac{dy}{dx} = ye^\frac{x}{y} - x[/tex]


    2. The attempt at a solution

    [tex]x dy = (ye^\frac{x}{y} - x) dx[/tex]

    [tex]x dy + ( -ye^\frac{x}{y} + x) dx[/tex]

    Using substitution
    [tex]x = vy[/tex]

    [tex]dx = vdy + ydv[/tex]


    [tex]vy dy + (-ye^v + vy) [ vdy + ydv ] = 0[/tex]


    [tex](vy + yv^2 - vye^v)dy + (vy^2 - y^2e^v )dv = 0[/tex]


    [tex](vy + yv^2 - vye^v)dy = (y^2e^v - vy^2 )dv[/tex]


    [tex]\frac{(y)(v + v^2 - ve^v)}{y^2(e^v - v)} dy = dv[/tex]


    [tex]\int \frac{1}{y} dy = \int \frac{(e^v - v)}{(v + v^2 - ve^v)} dv[/tex]

    The integral on the left side is easy to solve, but I can't find a way to solve the right side of the equation. Maybe i'm wrong in some earlier step...


    Any Suggestions?

    Thanks and sorry for my English, I'm still learning it (i'm from venezuela)
     
  2. jcsd
  3. Feb 26, 2010 #2

    LCKurtz

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    Science Advisor
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    Gold Member

    Your English is quite good; no need to apologize. For what it is worth, I agree with your steps, but I don't see how to work it either. Apparently, neither does Maple.
     
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