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I know that I shouldn't see $dx/dt$ as a fraction.

But we do this:

$dy/dx=y$

$dy/y=dx$

$ln(y)=x+c$

And we can use $dx$ and $dt$ when modeling something like: change in volume of balloon while pumping air in constant rate -

$dv=i \cdot dt$

$dr=dv/(4\pi r^2)$

and we can use $dv$ as small change in volume over small time and do this:

$dr=i\cdot dt/(4\pi r^2)$

But are these things possible? Do we encounter these? (I have just made up these equations, haven't seen them anywhere) and are we able to solve for $y$?

$dy=x^2dx+5x$

$dy\cdot dx=6xy$

$(dy)^2=\ln(5dx)$

Balarka Sen
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Nemexia
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1 Answers1

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$dy, dx$ stands for differentials of the variables $y$ and $x$ respectively, similar to any other variable. It's an infinitesimal quantity, usually used in linear approximation to represent a change in the linearization of a function.