Question

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

The linear DE, ${\mathit{y}}^{\cancel{\mathbf{c}}}\mathbf{-}\mathit{k}\mathit{y}\mathbf{=}\mathit{A}$, whereandare constants, is autonomous. The critical point of the equation is a(n) (attractor or repeller) for k > 0anda(n) (attractor or repeller) for k < 0.

Short answer

$-\frac{A}{k}$; repeller ; attractor

Step-by-step solution

Definition

A solution that starts near cis like a charged particle that, over time, is drawn to a particle of opposite charge, and so $c$ is also referred to as an attractor.

An unstable critical point is also called a repeller.

Step 2:

We have been given differential equation

Writing the differential equation in the form$y\text{'}=k\left(y+\frac{A}{k}\right)$we see that the critical point $-\frac{A}{k}$is a repeller for k < 0and an attractor for k < 0.