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Homework Help: Homogeneous DE simplification

  1. Jan 12, 2007 #1
    This is a basic simplification, but I'm going to post this here because it becomes homogeneous, and I know [tex]v = \frac{y}{x}[/tex] but I don't see this simplification, I don't understand how it gets from this...

    [tex]\frac{dy}{dx} = \frac{y-x}{y+x}[/tex]

    To THIS:

    [tex] = \frac{v-1}{v+1}[/tex] (I'm just only showing the RHS here)

    If someone wouldn't mind explaining it, that would be great because I'm lost, unless this is a special rule.
     
  2. jcsd
  3. Jan 12, 2007 #2

    cristo

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    Well, let y=vx, then sub into the RHS and you get [tex]\frac{vx-x}{vx+x}=\frac{x(v-1)}{x(v+1)}=\frac{v-1}{v+1}[/tex]
     
  4. Jan 12, 2007 #3
    oh wow, that's incredible, I get it, thanks cristo
     
  5. Jan 12, 2007 #4

    cristo

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    You're welcome!
     
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