anonymous
  • anonymous
"Since integral curves can’t cross an integral curve itself is both an upper and a lower fence" Can anyone explain this for me a little more. I'm not sure if i'm getting it right. I kind of understand this "An integral curve is also a fence of both types" The quote is a Remark in this http://ocw.mit.edu/courses/mathematics/18-03sc-differential-equations-fall-2011/unit-i-first-order-differential-equations/geometric-methods/MIT18_03SCF11_s2_5text.pdf
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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ganeshie8
  • ganeshie8
|dw:1437290124325:dw|
ganeshie8
  • ganeshie8
Because to go outside the fence requires to cross the fence; at the point of crossing, there will be two different slopes. But the direction field allows you to have only one slope at a point.
anonymous
  • anonymous
Thanks for answering, i knew that. I just got confused by that specific remark, like how an integral curve itself could be both an upper and a lower fence, arent the integral curve suppose to be between them (if conditions says so)

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ganeshie8
  • ganeshie8
so the solution curves inside the fence stay inside forever the solution curves outside the fence stay outside forever |dw:1437290828331:dw|
anonymous
  • anonymous
Oh. I think i get it now. So the red integral curve is algo being a lower fence for the purple integral curve.
anonymous
  • anonymous
Btw, i know that if an integral curve is inside a fence it never gets out, i'm just wondering about that specif remark saying an integral curve is also a fence
ganeshie8
  • ganeshie8
yes that follows from the fact that the integral curves cannot touch each other
anonymous
  • anonymous
Thanks, i think i understood
ganeshie8
  • ganeshie8
the fence shown in the diagram is indeed an integral curve
ganeshie8
  • ganeshie8
don't get tricked by the word "fence"
ganeshie8
  • ganeshie8
|dw:1437291167999:dw|
anonymous
  • anonymous
Sorry you lost me again
anonymous
  • anonymous
i meant i'm lost again xD
anonymous
  • anonymous
straight black lines are also integral curves, why?
ganeshie8
  • ganeshie8
Yes, they are integral curves, it is given.
anonymous
  • anonymous
Is it? it just says those lines are fences and that any integral curve between them will remaing there forever. How comes those fences are now integral curves.
ganeshie8
  • ganeshie8
If they are not integral curves, then there is nothing stopping to have a solution curve like this : |dw:1437291488143:dw|