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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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Please feel free to post as many doubts on our disucssion forum as you can. If you find any question difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We are all IITians and here to help you in your IIT JEE preparation. All the best. Regards, Naga Ramesh IIT Kgp - 2005 batch
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