Aah! Differential Equations : Graphics, Models, Data

New Suggestions for Section 2.5

On the same graph, sketch the functions 1 - y² and (1 - y²)(4 - y²).
(a) What does this suggest about solutions of dy/dx = 1 - y² and dy/dx = (1 - y²)(4 - y²), with y(0) = y₀, where |y₀| < 1?
(b) What happens if |y₀| > 1?