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The largest interval for which a certain solution is unique

  1. Jan 18, 2010 #1
    Hi, I need to find out what the largest interval in which the given intial value problem is certain to have a unique solution. I don't really know how to approach this problem though, I have a theorem on existence and uniquness of solutions but I'm finding it hard to make sense of it. I've got quite a few problems to have a look at, an example would be;

    xy[tex]^{''}[/tex] +4y = x, y(2)=1, y[tex]^{'}[/tex](2)=2

    Trying to make sense of the theorem I think the answer would be that the interval must be greater than equal to 1, but this is probably complete rubbish.

    Any help would be great! Thanks
     
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  3. Jan 20, 2010 #2

    LCKurtz

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    Why don't you state the theorem that you have to work with? You just have to check the hypotheses of the theorem against this particular equation. My guess would be x = 0 represents a problem.
     
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