Question

Answer Problems 1-12without referring back to the text. Fill in the blanks or answer true or false.

An example of an autonomous linear first-order DE with a single critical point -3is whereas an autonomous nonlinear first-order DE with a single critical point 3is

Short answer

Examples are$\frac{dy}{dx}=y+3\&\frac{dy}{dx}={\left(y+3\right)}^2$ & .

Step-by-step solution

Definition

An autonomous system or autonomous differential equation is a system of ordinary differential equations which does not explicitly depend on the independent variable.

Autonomous equation

An autonomous linear first-order DE with a single critical point -3 is$\frac{dy}{dx}=y+3$

An autonomous nonlinear first-order DE with a single critical point -3 is $\frac{dy}{dx}={\left(y+3\right)}^2$.