Hi,

I have the following equation

I found solutions .

I don't really get why it would not violate the existence and uniqueness theorem.

I would have .

Isn't f and f' continuous on R? If yes it should thus admit one solution.

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- Jan 25th 2009, 02:57 PMvincisonfireExistence and uniqueness theorem
Hi,

I have the following equation

I found solutions .

I don't really get why it would not violate the existence and uniqueness theorem.

I would have .

Isn't f and f' continuous on R? If yes it should thus admit one solution. - Jan 25th 2009, 03:39 PMNonCommAlg
1. you forgot that the existence and uniqueness theorem is for differential equations with initial condition! i guess in your problem it's

2. the function is not a solution to your differential equation. [solve your equation again!]

3. one reason that the solution is not unique is that is not continuous at and so it won't be continuous in any region containing that point.

4. basically there is no open rectangle containing in which is defined everywhere. - Jan 25th 2009, 04:00 PMvincisonfire
1. Yes sorry about that is the initial condition.

2.

But this does not satisfy the equation. Where am I mistaken?

3. & 4. Got it the largest "rectangle" is the point (0,1) where of course only one solution exists.