Separation of variables

Separation of variables is a technique to solve differential equations. It requires the equation to be separable; that is, the equation is of the form

$y'=F(y)G(t)$

where the RHS is the product of a function of y and a function of t.

It is considered to be easier than Integrating factor when both options are available.

Cases

Two notable cases are homogeneous linear first order ODEs and Autonomous ODEs.

Procedure

Divide both sides by $F(y)$, integrate, and you get an Implicit equation of y in terms of t.