# The largest interval for which a certain solution is unique

1. Jan 18, 2010

### 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

2. Jan 20, 2010

### 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.