A quote from the book of T.L. Chow 'Mathematical methods for physicists'(adsbygoogle = window.adsbygoogle || []).push({});

The reader may notice that dy/dx has been treated as if it were a ratio of dy and

dx, that can be manipulated independently. Mathematicians may be unhappy

about this treatment. But, if necessary, we can justify it by considering dy and

dx to represent small finite changes (delta)y and (delta)x, before we have actually reached the

limit where each becomes infinitesimal.

(instead of delta in parenthesis in the last sentence the latin letter delta is intended, just didn't know how to put it)

This part was from the chapter about differential equations. Can someone elaborate on this a little. I generally understand that the derivative is different than just the ratio of function change to it's argument change, but in which cases can we take it as a ratio of dy to dx and treat them independently without getting a wrong solution for the differential equation.

thanks

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# Are dy and dx in dy/dx independent? Please help

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