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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...

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