An **autonomous differential equation** is a differential equation that does not explicitly include the independent variable. If the independent variable is time, the equation is called time-invariant. First order autonomous differential equations of the form

- $ \frac{dy}{dt} = f(y) $

are very easy to solve, as they will always be separable. In addition, since *y(t)* will have a stationary point when *f(c) = 0* for some *c*, *y(t) = c* is a solution to the equation. Such a solution is known as the equilibrium solution, and are the only constant solutions of such an equation.

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