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Math Help - Homogenous Equation Help

  1. #1
    Junior Member
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    May 2009
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    Homogenous Equation Help

    Hey everyone
    I'm studying for a test tomorrow, and I need some help with a problem (im sure something of this sort will come up)

    -ydx+(x+\sqrt{xy})dx =0

    im using a substitution, where y = vx, but you still end up with a sqrt with 2 variables in it

    thanks
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  2. #2
    Junior Member
    Joined
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    Quote Originally Posted by TheUnfocusedOne View Post
    Hey everyone
    I'm studying for a test tomorrow, and I need some help with a problem (im sure something of this sort will come up)

    -ydx+(x+\sqrt{xy})dx =0

    im using a substitution, where y = vx, but you still end up with a sqrt with 2 variables in it

    thanks
    I assume you mean (there are two dx differentials):

    -ydx+(x+\sqrt{xy})dy =0

    Rewrite the equation first as:

    -\frac{y}{x}dx+(1+\sqrt{\frac{y}{x}})dy =0

    from which:

    \frac{dy}{dx}=\frac{\frac{y}{x}}{1+\sqrt{\frac{y}{  x}}}

    Then do your proposed substitution as:

    \frac{dy}{dx}=v+x\frac{dv}{dx}=\frac{v}{1+\sqrt{v}  }

    Solvable by separation of variables.

    Hope this gets you started,

    Coomast
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  3. #3
    Junior Member
    Joined
    May 2009
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    gah, idiot
    i was trying something like that


    thanks
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