/sci/ - Science & Math

>>11354310
>>11352148

Okay, I think I've got it now, someone just check me on this:

I understood the gist of PDEs, because you've got a relationship of derivatives of multiple variables and you look for antiderivative(?) solutions with respect to each variable. When it came to ODEs though, I kept seeing simple examples like f'(x) = x^2, for which the solution is (x^3)/3. When I saw these examples I wondered what the difference was from a function, the term ODE and process of finding a solution is redundant to getting the antiderivative of a derivative.

But that's an absolutely trivial ODE that exists only for learning purposes. A more common/practical situation would be one where I have two functions f(x) and g(x), for which I have not observed any relationship, but I do have the relationship of their derivatives, say f'(x) = 5 sin g'(x). This is an ODE from which I would search for the equation (antiderivative?) describing a function z(x) (which may be one of many or may not exist in entirety) which is the relation of f(x) and g(x).

Am I hitting the mark here?

I know It probably seems like I'm overshooting my level of understanding, but I tend to digest subjects best from an overview of everything in a book at once to see how stuff links up from above before grinding on exercises to get an actual working knowledge of how things behave.