Question in understanding differitial equations

  • #1
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Main Question or Discussion Point

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

????
 

Answers and Replies

  • #2
Hootenanny
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It looks very much like an http://mathworld.wolfram.com/ExactDifferential.html" [Broken] to me.
 
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  • #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.
 
  • #4
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i too see it as an exact differential
it looks like the one in the article

why its not an exact differential??
 
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  • #5
Defennder
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They differ by a factor of -1.
 
  • #6
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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?
 
  • #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.
 
  • #8
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what does the expression d/dx represent

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

???
 
  • #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
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?
 
  • #12
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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
???
 
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  • #13
Defennder
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I really have no idea what you are saying. What patterns of integrals are you talking about?
 
  • #14
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i/x i recognized as the derivative of ln|x|

how to solve this correctly
 
  • #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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