How to tell if an equation is autonomous

The equation is autonomous, since the independent variable ( ) does not explicitly appear in the equation. To plot the slope field and isocline for this equation, one can use the following code

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8. Autonomous and non-autonomous first order differential

A differential equation or system of ordinary differential equations is said to be autonomous if it does not explicitly contain the independent variable (usually denoted t). A

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Autonomous Differential Equations

Autonomous Equation: A differential equation where the independent variable does not explicitly appear in its expression. It has the general form of y′ = f (y). Examples: y′ = e2y − y3 y′ = y3 − 4 y

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Autonomous Differential Equations

LECTURE 5: AUTONOMOUS EQUATIONS 3 y = (0 if x ≤1 (x−1)2 4 if x ≥1 This is also a solution. And in fact, you can replace “1” by any con-stant C ≥0 and still get a solution, so in fact there

Introduction to autonomous differential equations

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