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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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