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why should dy/dx not regarded as quotient of dy and dx

why should dy/dx not regarded as quotient of dy and dx

Grade:Upto college level

1 Answers

Ramesh V
70 Points
12 years ago

Dear Sudarshan,

In my view, It isn't a fraction because crudely, a fraction is a ratio of two numbers, a/b, and neither dy nor dx are numbers. But, you can under certain special circumstances treat it like a fraction. It is perfectly acceptable to do so for practical purposes and all we are all doing  this:

rearrange your Differential Equation to the following form:

                        f(y).dy/dx=g(x)              for some functions of f and g.

Now, on integrating both sides with respect to x

\integral f(y) . \fraction{dy}/{dx}.dx = \integral g(x).dx

but the one on the left is exactly the same as  \integral f(y)dy

so you can just pretend  that the dx's cancel out. Technically they do cancel out but not because it's a fraction, but because of what the symbols mean as calculus tools.

Regards,

 

Its really a good question, but i think you don't really need to know all this to use this technique, and this is why it is usually not explained in detail. you might look at some books  for a simpler explanation if you are still curious.

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Regards,
Naga Ramesh
IIT Kgp - 2005 batch

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