"Factoring" a differential equationpic.twitter.com/1DymALdtCc
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You can also do this for a 4th-order DE (useful for describing bending waves in plates):pic.twitter.com/o3i88b8uem
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I'm rusty. Aren't these just examples of solving the characteristic equation? Or is this about how neat the solution turns out in terms of k?
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I think the neat thing is that you can factorise a differential operator in the same way that you'd factorise a polynomial, and then solve it easily. There's nothing terribly deep here, but it's a nifty trick to have in your toolkit.
End of conversation
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