Given the Exact Differential $$M(x,y) \, dx + N(x,y) \, dy = 0\tag 1$$
I noticed that at least in Mathematica, the solution $\phi(x,y)$ can be found via solving the following differential equation from manipulation of $(1)$.
$$ \frac{dy}{dx} \equiv \frac{-M(x,y)}{N(x,y)} $$ I'm Standard Form, dropping $(x,y)$, $$ \frac{dy}{dx} + \frac{M}{N} \equiv 0$$ In Mathematica:
DSolve[y'[x]== -m[x,y[x]]/n[x,y[x]],y[x],x]
Is this commonly known, used, and if so, what is it called? Thank you all very much. I am starting to feel as though this should be in the Mathematica SE. If others believe so, please vote to move.
I could see that Mathematica users (and perhaps other CAS users) might find it useful, but there is no name for it even though it is well known.