>>11532250>Why is it that many of the physical phenomena we observe is modeled by first and second degree differential equations? Is it just the best fit we can find, or is there some deeper reason for this? Do we use differential equations because we find them (relatively) easy to work with when describing things?Well. For ODEs the answer is very obvious, because any ODE can be written as a system of first order ODEs.
For PDEs the question becomes obviously a lot more tricky. And I do not think the answer is obvious, surely sometimes you can rephrase PDEs of higher order as PDEs of lower order, but in general I think we are not looking for very complex relationships, but rather simple one, so most of the stuff we find will relate to first or second order PDEs.
>>11532283False.
That is only the case for ODEs.
Much of PDE theory is just for the case of first/second derivative and there is no general way to lower the order of a PDE.
If you can prove me wrong by "thinking hard enough" you are pretty much guranteed a Fields medal, because you just revolutionized about 100 years of Analysis research.
