Hi everyone,

I'm having trouble with the ideas involved with the uniquesness theorem for a linear nth order IVP.

As an example:

The initial value problem

$\displaystyle 3y'''+5y''-y'+7y=0,$ $\displaystyle y(1)=0$, $\displaystyle y'(1)=0,$ $\displaystyle y''(1)=0$.

Now, I can see that $\displaystyle y=0$ is a trivial solution here, but by the theorem, this has got to be the ONLY solution on any interval containing 1. I don't see this. Is this true? Is there no other solution to this problem ?