The largest interval for which a certain solution is unique

[Juggler123]

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^{''} +4y = x, y(2)=1, y^{'}(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

 

[LCKurtz]

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.