Separable DEs

With functions in the form

f (y) \frac{d y}{d t} = g (t)

Integrating both sides with respect to t:

\int f (y) \frac{d y}{d t} d t = \int g (t) d t \to \int f (y) d y = \int g (t) d t

by the change of variables theorem
So,

\ln | A | = b + C \to A = c e^{b}

Integrating Factor