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Re:Quantum Physicists Explained Earth’s Oscillating Weather ... by aeternum on Wednesday July 19, 2023 @12:19AM (#36782073)
First order differential equations generally govern diffusion where energy spreads out over an area. Second order are often waves where energy propagates but does not diffuse.

Is pretty much everything described by those two classes?

Any third-order differential equations in physics?

Re:Quantum Physicists Explained Earth’s Oscillating Weather ... by defrost on Wednesday July 19, 2023 @12:31AM (#36782138)
Good question.

First & second order covers most cases, third order applications include things with 'jerk', sticky flows through small channels, ..

There are other examples offered here:

https://www.researchgate.net/post/Are_there_examples_of_thir...

https://www.quora.com/Why-dont-differential-equations-of-phy...

https://math.stackexchange.com/questions/2167292/are-there-e...