# Properties of Direction Field of a Separable Differential Equation

I am investigating the general properties of the direction field of a separable differentiable equation. Is there some direct correlation between the equation being separable and the invariance in translation of the direction field? To illustrate, how can I figure out which $$3$$ of the direction fields below are that of separable differential equations?

• Note that nullclines of separable equation $\frac{dy}{dx} = \frac{f(x)}{g(y)}$ are only straight vertical or horizontal lines. Look at nullclines on these pictures, that will help. – Evgeny Jan 31 at 8:25