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1st order, non linear, homogeneous, ODE

  1. Oct 13, 2008 #1
    1. The problem statement, all variables and given/known data

    "Solve the following ODE's:"
    "3u+(u+x)u'=0"

    This is our first weeks homework and he went this through this so quickly in class.

    2. Relevant equations

    None. x and u are both variables.

    3. The attempt at a solution
    I know it is homogeneous and non linear. I tried v-substitution and just couldn't get a v to fit. Do i need to use the method of integration factor?

    Thanks guys!
     
    Last edited: Oct 13, 2008
  2. jcsd
  3. Oct 13, 2008 #2

    Defennder

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    Homework Helper

    Why doesn't this work? What do you understand by v-substitution?
     
  4. Oct 13, 2008 #3
    Not much, I feel like I'm guessing... any suggestions what i should substitute?
     
  5. Oct 13, 2008 #4

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Perhaps better to rewrite it as
    [tex]u'= \frac{-3u}{u+x}= \frac{-3\frac{u}{x}}{\frac{u}{x}+ 1}[/tex]

     
  6. Oct 13, 2008 #5
    -(1/4)ln|(u/x)|=ln|x|+c ?

    Thanks so much. This class is like diffy eq on steroids and wasn't very good at diffy eq.
     
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