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? enter image description here

  • $\begingroup$ 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. $\endgroup$ – Evgeny Jan 31 at 8:25

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