I was watching the video linked below. I am confused around part 32:50. The differential is being rewritten as the derivatives of two other quantities. This is where I get confused. What is the point of rewriting terms in a differential equation as derivatives of something else? I understand in the video how he rewrote the first term, but for the second term he introduces a quantity that I don't understand. Can anyone help?
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Welcome to MSE. Please edit and use MathJax to properly format math expressions. – Lee David Chung Lin Mar 13 '19 at 00:39
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You have already asked a question in https://math.stackexchange.com/q/247866 concerning this video. Without having seen the video, you must know that second order differential equation(s) are most often treated by translating them as systems of first order differential equations. – Jean Marie Mar 13 '19 at 02:42