The fundamental set
Hi, I've been looking for a good proof showing that there exists a fundamental set for an nth order linear homogeneous ODE. That is, that there exists n linearly dependent solutions for any nth order Homogeneous linear ODE.
I can't seem to find what I'm looking for on google. I just want a good argument saying that there are always n solutions to an nth order.
Well, I don't know if the claim is true or not, but if it is, I'm pretty sure you can find a proof of it in Coddington and Levinson. Alas, my copy is at work, so I can't look it up for you. Look for "fundamental matrix." It's definitely true for the constant-coefficient case.