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Question in understanding differitial equations

  1. May 11, 2008 #1
    i have started to learn this stuff
    and it looks like a normal derivative stuff but its different
    i dont know how to find a general solution
    what is the algorithm to act on??

    here is a simple example:
    http://img381.imageshack.us/my.php?image=26202865up1.jpg
    i was told to find a general solution

    i dont know how to isolate Y i am not sure
    what i need to do here
    its so much different

    ????
     
  2. jcsd
  3. May 11, 2008 #2

    Hootenanny

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  4. May 11, 2008 #3

    Defennder

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    No, it's not an exact differential equation... yet. You have to multiply the entire expression throughout by something to make it exact, then you can solve it by that method.
     
  5. May 11, 2008 #4
    i too see it as an exact differential
    it looks like the one in the article

    why its not an exact differential??
     
    Last edited: May 11, 2008
  6. May 12, 2008 #5

    Defennder

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    They differ by a factor of -1.
     
  7. May 12, 2008 #6
    how did you get -1??

    there are two variables here
    there could be also derivatives in one of them

    how did you get the factor?
     
  8. May 12, 2008 #7

    Defennder

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    I did this: [tex]\frac{\partial}{\partial y} \ \frac{y}{x} = \frac{1}{x}[/tex]
    [tex]\frac{\partial}{\partial x}\ \left(y^2-lnx\right) = -\frac{1}{x}[/tex].

    That's why I said they differ by factor of -1.
     
  9. May 12, 2008 #8
    what does the expression d/dx represent

    when i did derivatives there were only dx not "d"

    ???
     
  10. May 12, 2008 #9

    Defennder

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    Uh, which expression? This one: [tex]\frac{\partial}{\partial x} [/tex]? That's partial differentiation. It means to say differentiate a multi-variable function with respect to x alone.
     
  11. May 13, 2008 #10
  12. May 14, 2008 #11

    Defennder

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    Actually I don't know what you're writing:

    Specifically, what does [tex]d(ln|y|) \ \mbox{and} \ d(ln|x|)[/tex] mean?
     
  13. May 14, 2008 #12
    i recognized 1/x and 1/y as a derivatives of ln|x| and ln|y|

    thats the only integrals i saw there

    i read that i am supposed to see patterns of integrals
    and solve them

    but its not working here
    ???
     
    Last edited: May 14, 2008
  14. May 14, 2008 #13

    Defennder

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    I really have no idea what you are saying. What patterns of integrals are you talking about?
     
  15. May 14, 2008 #14
    i/x i recognized as the derivative of ln|x|

    how to solve this correctly
     
  16. May 14, 2008 #15

    Defennder

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    I don't know how that is related to this question. I'll just refer you to these notes, then maybe you can apply the technique here.

    A differential equation of the form [tex]N(x,y) \ dy + \ M(x,y) \ dx =0[/tex] is considered exact if [tex]\frac{\partial M}{\partial y} \ = \ \frac{\partial N}{\partial x}[/tex].

    Eg. [tex]x \ dy -y \ dx = 0[/tex] is not exact. But it can be made to be exact by multiplying throughout by the 1/x^2:

    [tex]\frac{1}{x} \ dy - \frac{y}{x^2} \ dx = 0[/tex]

    See here for more details on the topic:
    http://tutorial.math.lamar.edu/Classes/DE/Exact.aspx
     
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