The solution of differential equations by separation of variables in physics is also notated in an abusive way. You have some differential equation

dy/dx = g(x)h(y)

You separate the variables by some quick manipulations

dy/h(y) = g(x) dx

And then you have a small step in some coordinate on both sides. So by integrating both sides

\int 1/h(y) dy = \int g(x) dx

you find a solution to your differential equation. Obviously there's a real formal procedure underneath it with also some safeguards. For example you're supposed to check that h(y) doesn't equal 0 at any point. But the happy path in physics is often done without worrying about all that.