1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Staff Emeritus
    Science Advisor

    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

    User Avatar
    Staff Emeritus
    Science Advisor

    You're welcome!
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook