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Separable Equation

  • Thread starter 2RIP
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  • #1
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Homework Statement


Solve y'=y^2/x , y(1)=1 and give the largest x-interval on which the solution y(x) is defined.


Homework Equations





The Attempt at a Solution


[tex]dy/dx = y^{2}/x[/tex]
[tex]\int dy/y^{2}= \int dx/x[/tex]
[tex]y=1/(1-ln|x|)
[/tex]

Therefore, i find intervals [tex](\infty, e), (0,e), (- \infty , -e)[/tex] where y(x) is defined.

so would the intervals to choose be [tex](\infty, e) & (- \infty , -e)[/tex]??

Thanks
 
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Answers and Replies

  • #2
tiny-tim
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[tex]dy/dx = y^{2}/x[/tex]
[tex]\int dy/y= \int dx/x[/tex]
Hi 2RIP! :smile:

erm … what happend to the y2? :rolleyes:
 
  • #3
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Oh sorry, i was still learning how to use the latex coding and left it out. But the rest of my solution should be correct.

Thanks for pointing that out.
 
  • #4
tiny-tim
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Homework Statement


Solve y'=y^2/x , y(1)=1 and give the largest x-interval on which the solution y(x) is defined.

[tex]y=1/(1-ln|x|)
[/tex]
Therefore, i find intervals [tex](\infty, e), (0,e), (- \infty , -e)[/tex] where y(x) is defined.

so would the intervals to choose be [tex](\infty, e) & (- \infty , -e)[/tex]?
Hi 2RIP! :smile:

y is defined at x = 0 , isn't it?

I'm a little confused by the question … the two largest intervals are both infinite …

I suspect they mean the largest interval containing x = 1.

I'm not sure, though … :redface:
 

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