I'm a bit confused about why these types of problems are presented the way they are.
First order linear differential equation:
$$dy/dt + p(t) y = g(t);$$
First order separable differential equation:
$$M(t) + N(y)dy/dt = 0.$$
How are these related? I think if we take $N(y) = 1/y, M(t) = p(t)$ and $g(t)=0$, then the first order linear differential equation is separable. Is there some sort of deeper connection here that I'm missing?