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 $y$?
$dy=x^2dx+5x$
$dy\cdot dx=6xy$
$(dy)^2=\ln(5dx)$