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Oracle
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posted by  Ctrl on 7/2/2008 10:45:08 PM  |  status: Closed  

Please Explain: Existence and uniqueness of solution

Course Textbook Chapter Problem
Differential Equations Differential Equations (6th Ed), Nagle, Saff, Snider 1.2 25
Question Details:
in my book theorem 1 says:

Given the initial value problem
,    

assume that and are continuous functions in a rectangle
that contains the point .  Then the initial value problem has a unique solution in some interval , where δ is a positive number.
------------------------------
now the problem:

Determine whether Theorem 1 implies that the given initial value problem has a unique solution.


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what i did was to isolate , when i did that i got

so it is not continuous when x=0

Does this mean that the initial problem has a solution?  If so please explain, and also write the Region in set builder notation

thanks in advance

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Scholar
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posted by potter40 on 7/2/2008 10:48:08 PM  |  status: Live
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Ctrl's comment:
"yea, would you care to elaborate tho? I know that gives me 4*t*x^-2, but that doesn't answer my question"
Response Details:

Would integrating both sides not give you a solution in terms of x?
Oracle
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posted by Bpanda on 7/3/2008 12:00:35 AM  |  status: Live
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Ctrl's comment:
"thank you"
Response Details:
 
===>
 
===>
 
===>
 
where C is a constant of integration that can be determined by the initial condition x(2) = -π
 
===>     ===>  
 
thus :  
 
----> 
 
hope this helps
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